datasets/GARCH.ipynb

{
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  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "ir",
      "display_name": "R"
    },
    "language_info": {
      "name": "R"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Modelos GARCH\n",
        "\n",
        "- Os modelos  ARCH(m) vistos anteriormente tem a característica de que, na prática, precisa-se de um valor de $m$ muito grande.\n",
        "- Para resolver este problema, Bollerslev (1986) propôs uma generalizacão do modelo ARCH, chamada de GARCH (Generalized ARCH).\n",
        "- O modelo é mais parcimonioso e têm um melhor desempenho do que os modelos ARCH."
      ],
      "metadata": {
        "id": "DHYuDQ2aFtFZ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Definicão:** Um modelo GARCH(p,q) é definido por \n",
        "\\begin{align*}\n",
        "r_t &= \\sigma_t \\epsilon_t \\\\\n",
        "\\sigma_t^2 &= \\omega + \\displaystyle \\sum_{i = 1}^p \\alpha_i r_{t-i}^2 + \\sum_{j = 1}^q \\beta_j \\sigma_{t-j}^2,\n",
        "\\end{align*} em que $\\epsilon_t$ é _iid_ com média zero e variância 1, $\\omega > 0$, $\\alpha_i, \\beta_j \\geq 0$ e $\\alpha_1 + \\cdots + \\alpha_p + \\beta_1 + \\cdots + \\beta_q < 1$ (condicão sufiente de estacionariedade)."
      ],
      "metadata": {
        "id": "9TH6a1rsJo4B"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Observacão:** Note que um GARCH(p,q) pode escrito na forma de um ARMA.\n",
        "\n",
        "- Defina $\\nu_t = r_t^2 - h_t$\n",
        "- $r_t^2 = \\omega + \\displaystyle \\sum_{i = 1}^k(\\alpha_i + \\beta_i)r_{t-i}^2 + \\nu_t - \\sum_{j = 1}^q \\beta_j \\nu_{t-j},$ em que $k = max(p,q).$"
      ],
      "metadata": {
        "id": "iomjRubxM0G2"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Propriedades\n",
        "\n",
        "- $\\mathbb{E}(r_t) = 0$\n",
        "- $\\mathbb{V}(r_t) = \\mathbb{E}(r_t^2) = \\dfrac{\\omega}{1 - \\alpha_1 - \\cdots - \\alpha_p - \\beta_1 - \\cdots - \\beta_q}$\n",
        "- $\\mathbb{C}ov(r_t, r_{t+k}) = 0, \\quad \\forall k$ \n",
        "\n",
        "> Na prática, utilizamos valoes de $p$ e $q$ baixos. Por exemplo: GARCH(1, 1), GARCH(1, 2), GARCH(2, 1), GARCH(2, 2). **Na maioria da aplicacões o GARCH(1, 1) é suficiente.**"
      ],
      "metadata": {
        "id": "9YG-1YYqRcxP"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Identificaão:\n",
        "\n",
        "- A identificacão segue o já aprendido no modelo ARCH (devemos verificar se a variância condicional precisa ser modelada).\n",
        "- Identificar a ordem do modleo GARCH não é tão facil (embora pode-se seguir o mesmo procedimento utilizado para modelos ARMA devido à forma alternataiva de escrever o modelo GARCH). \n",
        "- A prática commúm é ajustar modelos GARCH de ordem baixa e utilizar algum criterio de informacão (AIC, BIC, AICc) para escolher, dentre os modelos que capturaram apropriadamente a dinânica dos dados, o melhor. Outra opcao pode ser através de validacão cruzada para séries temporais."
      ],
      "metadata": {
        "id": "DQPgmoPHYOnM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Estimacão:\n",
        "\n",
        "Pode ser feita por máxima verossimilhanca condicional. Se $\\Theta = (\\omega, \\alpha_1, \\cdots, \\alpha_p, \\beta_1, \\cdots, \\beta_q)$,\n",
        "$$L(\\Theta) = \\displaystyle \\prod_{i = p+1}^T f(r_i | \\mathcal{F}_{i-1})$$\n",
        "\n",
        "$$l(\\Theta) = \\displaystyle \\sum_{i = p+1}^T \\log(f(r_i | \\mathcal{F}_{i-1})),$$ em que, para $k = 1, \\cdots, q$, $\\sigma_k^2 = \\hat{\\sigma}^2 = \\mathbb{V}(r_k)$ ou a variância amostral.\n",
        "\n",
        "\n",
        "No caso de normalidade, \n",
        "\n",
        "$$l(\\Theta) \\propto - \\sum_{i = p+1}^T \\log(\\sigma_i^2) -  \\sum_{i = p+1}^T \\dfrac{r_i^2}{\\sigma_i^2}$$\n",
        "\n",
        "> **Como fariamos a implementacão computacional?**"
      ],
      "metadata": {
        "id": "KDnocJwPZlhq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Simulando GARCH\n",
        "install.packages(\"TSA\")\n",
        "library(TSA)"
      ],
      "metadata": {
        "id": "-a0MPdBJndPN",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c577fa23-da71-46ef-992c-2a381bc616c3"
      },
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Installing package into ‘/usr/local/lib/R/site-library’\n",
            "(as ‘lib’ is unspecified)\n",
            "\n",
            "also installing the dependencies ‘xts’, ‘TTR’, ‘quadprog’, ‘zoo’, ‘quantmod’, ‘leaps’, ‘locfit’, ‘tseries’\n",
            "\n",
            "\n",
            "\n",
            "Attaching package: ‘TSA’\n",
            "\n",
            "\n",
            "The following objects are masked from ‘package:stats’:\n",
            "\n",
            "    acf, arima\n",
            "\n",
            "\n",
            "The following object is masked from ‘package:utils’:\n",
            "\n",
            "    tar\n",
            "\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "set.seed(123)\n",
        "serie = garch.sim(alpha = c(.005, 0.08), beta = 0.85, n = 1000)"
      ],
      "metadata": {
        "id": "Lpb2AB3-n2bd"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "ts.plot(serie)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "b6flw0r_oGJV",
        "outputId": "526d23ec-c1e5-407c-894e-0cf588d87921"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "plot without title"
            ],
            "image/png": 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Mic8LPn2G74c0gt/PlgdeSehJ8yXsXA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\nT25E9gmIxbCvLDrmmsh+rN6Th2MJS+oMceIadVEyn0zRzXB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A11Af7x6F5yNzHEw3vAtiR6imZiB9yMmZ2iVGqsmTAyJPcIV+308Sn62I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"
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "op = par(mfrow = c(1,2))\n",
        "acf(serie)\n",
        "acf(serie^2)\n",
        "par(op)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "88ZAj71koIcq",
        "outputId": "e441f436-3c94-433d-976d-8b2fd0a107e4"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Series serie^2”"
            ],
            "image/png": 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RN/q6i44eabbxYgN7t27QoNDTWZTBqN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          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ll_garch11 = function(r, params) {\n",
        "  n = length(r)\n",
        "  sigma2 = rep(0, n)\n",
        "  ll = rep(0, n - 1)\n",
        "  sigma2[1] = var(r)\n",
        "  for (i in 2:n) {\n",
        "    sigma2[i] = params[1] + params[2]*r[i-1]^2 + params[3]*sigma2[i-1]\n",
        "    ll[i-1] = -log(sigma2[i]) - r[i]^2/sigma2[i]\n",
        "  }\n",
        "  log_veross = -sum(ll)  # Para minimizar o negativo da log-veross\n",
        "}\n"
      ],
      "metadata": {
        "id": "h1Uk_BhOkoRS"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "par_ini = c(0.005, 0.1, 0.8)\n",
        "optim(par_ini, ll_garch11, r = serie)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "S9-uOyZeoEJL",
        "outputId": "24f3111c-537a-4918-e241-5d225a8fd670"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\u001b[1;30;43mStreaming output truncated to the last 5000 lines.\u001b[0m\n",
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            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n",
            "Warning message in log(sigma2[i]):\n",
            "“NaNs produced”\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<dl>\n",
              "\t<dt>$par</dt>\n",
              "\t\t<dd><style>\n",
              ".list-inline {list-style: none; margin:0; padding: 0}\n",
              ".list-inline>li {display: inline-block}\n",
              ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
              "</style>\n",
              "<ol class=list-inline><li>0.00874359589783601</li><li>0.06006882137023</li><li>0.815243932685321</li></ol>\n",
              "</dd>\n",
              "\t<dt>$value</dt>\n",
              "\t\t<dd>-1673.6666215441</dd>\n",
              "\t<dt>$counts</dt>\n",
              "\t\t<dd><style>\n",
              ".dl-inline {width: auto; margin:0; padding: 0}\n",
              ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
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              ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
              "</style><dl class=dl-inline><dt>function</dt><dd>130</dd><dt>gradient</dt><dd>&lt;NA&gt;</dd></dl>\n",
              "</dd>\n",
              "\t<dt>$convergence</dt>\n",
              "\t\t<dd>0</dd>\n",
              "\t<dt>$message</dt>\n",
              "\t\t<dd>NULL</dd>\n",
              "</dl>\n"
            ],
            "text/markdown": "$par\n:   1. 0.00874359589783601\n2. 0.06006882137023\n3. 0.815243932685321\n\n\n\n$value\n:   -1673.6666215441\n$counts\n:   function\n:   130gradient\n:   &lt;NA&gt;\n\n\n$convergence\n:   0\n$message\n:   NULL\n\n\n",
            "text/latex": "\\begin{description}\n\\item[\\$par] \\begin{enumerate*}\n\\item 0.00874359589783601\n\\item 0.06006882137023\n\\item 0.815243932685321\n\\end{enumerate*}\n\n\\item[\\$value] -1673.6666215441\n\\item[\\$counts] \\begin{description*}\n\\item[function] 130\n\\item[gradient] <NA>\n\\end{description*}\n\n\\item[\\$convergence] 0\n\\item[\\$message] NULL\n\\end{description}\n",
            "text/plain": [
              "$par\n",
              "[1] 0.008743596 0.060068821 0.815243933\n",
              "\n",
              "$value\n",
              "[1] -1673.667\n",
              "\n",
              "$counts\n",
              "function gradient \n",
              "     130       NA \n",
              "\n",
              "$convergence\n",
              "[1] 0\n",
              "\n",
              "$message\n",
              "NULL\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Previsão\n",
        "\n",
        "Säo calculadas de forma similar ao modelo ARCH, _i.e,_ de forma recursiva. Por exemplo, para o caso GARCH(1, 1):\n",
        "\n",
        "- $\\hat{\\sigma}_{T+1|T} = \\hat{\\omega} + \\hat{\\alpha} r_{T}^2 + \\hat{\\beta}\\hat{\\sigma}_T^2$\n",
        "- $\\hat{\\sigma}_{T+k|T} = \\hat{\\omega} + \\hat{\\alpha} r_{T+k-1}^2 + \\hat{\\beta}\\hat{\\sigma}_{T+k-1}^2$"
      ],
      "metadata": {
        "id": "_BKHVM15fs83"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "> É commum termos nas aplicacões práticas que $\\alpha + \\beta ≈ 1$. Se  $\\alpha + \\beta + 1$, temos o modelo IGARCH   \\begin{align*}\n",
        "r_t &= \\sigma_t \\epsilon_t \\\\\n",
        "\\sigma_t^2 &= \\omega +  (1 - \\beta) r_{t-1}^2 + \\beta \\sigma_{t-1}^2,\n",
        "\\end{align*} com $0 < \\beta < 1$"
      ],
      "metadata": {
        "id": "bbTgrYWghjyJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "install.packages(\"rugarch\")\n",
        "library(rugarch)"
      ],
      "metadata": {
        "id": "eKkhshYspkZ6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "07c5075b-250e-400d-a5cc-b476a5afc39a"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Installing package into ‘/usr/local/lib/R/site-library’\n",
            "(as ‘lib’ is unspecified)\n",
            "\n",
            "also installing the dependencies ‘misc3d’, ‘truncnorm’, ‘FNN’, ‘kernlab’, ‘mclust’, ‘multicool’, ‘mvtnorm’, ‘plot3D’, ‘pracma’, ‘DistributionUtils’, ‘GeneralizedHyperbolic’, ‘Rsolnp’, ‘ks’, ‘numDeriv’, ‘spd’, ‘chron’, ‘SkewHyperbolic’, ‘Rcpp’, ‘RcppArmadillo’\n",
            "\n",
            "\n",
            "Loading required package: parallel\n",
            "\n",
            "\n",
            "Attaching package: ‘rugarch’\n",
            "\n",
            "\n",
            "The following object is masked from ‘package:stats’:\n",
            "\n",
            "    sigma\n",
            "\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "spec <- ugarchspec(mean.model = list(armaOrder = c(0, 0), include.mean = FALSE),\n",
        "                   variance.model = list(model = 'sGARCH', garchOrder = c(1, 1)),\n",
        "                   distribution = 'norm')"
      ],
      "metadata": {
        "id": "3fDcZMdeqq81"
      },
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "summary(serie)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "AarG2b7ArdV3",
        "outputId": "dafe11e2-593d-42b8-9877-b201f4e6f8cc"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. \n",
              "-0.743694 -0.166201  0.005876  0.006488  0.179236  1.021316 "
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "serie_c = scale(serie, center = TRUE, scale = FALSE)"
      ],
      "metadata": {
        "id": "XJYXZTObrgQV"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fit_01 <- ugarchfit(spec, serie_c, solver = 'hybrid')"
      ],
      "metadata": {
        "id": "sbWgJ5t7rZRr"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fit_01"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "USSTrvscrnhH",
        "outputId": "8e45bba3-0657-48f7-a3ce-c5fc1a604734"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "*---------------------------------*\n",
              "*          GARCH Model Fit        *\n",
              "*---------------------------------*\n",
              "\n",
              "Conditional Variance Dynamics \t\n",
              "-----------------------------------\n",
              "GARCH Model\t: sGARCH(1,1)\n",
              "Mean Model\t: ARFIMA(0,0,0)\n",
              "Distribution\t: norm \n",
              "\n",
              "Optimal Parameters\n",
              "------------------------------------\n",
              "        Estimate  Std. Error  t value Pr(>|t|)\n",
              "omega   0.008876    0.007175   1.2370 0.216097\n",
              "alpha1  0.059739    0.027512   2.1714 0.029903\n",
              "beta1   0.813572    0.122902   6.6197 0.000000\n",
              "\n",
              "Robust Standard Errors:\n",
              "        Estimate  Std. Error  t value Pr(>|t|)\n",
              "omega   0.008876    0.007953   1.1161 0.264391\n",
              "alpha1  0.059739    0.030821   1.9382 0.052596\n",
              "beta1   0.813572    0.136827   5.9460 0.000000\n",
              "\n",
              "LogLikelihood : -80.96887 \n",
              "\n",
              "Information Criteria\n",
              "------------------------------------\n",
              "                    \n",
              "Akaike       0.16794\n",
              "Bayes        0.18266\n",
              "Shibata      0.16792\n",
              "Hannan-Quinn 0.17353\n",
              "\n",
              "Weighted Ljung-Box Test on Standardized Residuals\n",
              "------------------------------------\n",
              "                        statistic p-value\n",
              "Lag[1]                      1.325  0.2496\n",
              "Lag[2*(p+q)+(p+q)-1][2]     1.593  0.3402\n",
              "Lag[4*(p+q)+(p+q)-1][5]     2.441  0.5185\n",
              "d.o.f=0\n",
              "H0 : No serial correlation\n",
              "\n",
              "Weighted Ljung-Box Test on Standardized Squared Residuals\n",
              "------------------------------------\n",
              "                        statistic p-value\n",
              "Lag[1]                     0.9291  0.3351\n",
              "Lag[2*(p+q)+(p+q)-1][5]    3.8456  0.2740\n",
              "Lag[4*(p+q)+(p+q)-1][9]    5.7842  0.3238\n",
              "d.o.f=2\n",
              "\n",
              "Weighted ARCH LM Tests\n",
              "------------------------------------\n",
              "            Statistic Shape Scale P-Value\n",
              "ARCH Lag[3]     2.291 0.500 2.000  0.1301\n",
              "ARCH Lag[5]     4.060 1.440 1.667  0.1686\n",
              "ARCH Lag[7]     4.767 2.315 1.543  0.2491\n",
              "\n",
              "Nyblom stability test\n",
              "------------------------------------\n",
              "Joint Statistic:  0.304\n",
              "Individual Statistics:             \n",
              "omega  0.2114\n",
              "alpha1 0.2224\n",
              "beta1  0.2136\n",
              "\n",
              "Asymptotic Critical Values (10% 5% 1%)\n",
              "Joint Statistic:     \t 0.846 1.01 1.35\n",
              "Individual Statistic:\t 0.35 0.47 0.75\n",
              "\n",
              "Sign Bias Test\n",
              "------------------------------------\n",
              "                   t-value   prob sig\n",
              "Sign Bias           0.5313 0.5953    \n",
              "Negative Sign Bias  0.1315 0.8954    \n",
              "Positive Sign Bias  0.7570 0.4492    \n",
              "Joint Effect        0.5961 0.8973    \n",
              "\n",
              "\n",
              "Adjusted Pearson Goodness-of-Fit Test:\n",
              "------------------------------------\n",
              "  group statistic p-value(g-1)\n",
              "1    20     10.92       0.9265\n",
              "2    30     23.24       0.7654\n",
              "3    40     29.44       0.8663\n",
              "4    50     44.50       0.6559\n",
              "\n",
              "\n",
              "Elapsed time : 0.1189475 \n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "e_hat = fit_01@fit$residuals/fit_01@fit$sigma\n",
        "op = par(mfrow = c(1,2))\n",
        "acf(e_hat)\n",
        "acf(e_hat^2)\n",
        "par(op)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "JVfNghsvscld",
        "outputId": "12660013-8f8f-4f24-bd4b-5d48e8db5e36"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Series e_hat^2”"
            ],
            "image/png": 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vnTn/40bdq0tkPnzp27+eabd+7cOXPmTLHiAUCfCA0NXb9+/ZQpUxYtWuTk5NRu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\n"
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "qqnorm(e_hat)\n",
        "qqline(e_hat)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "fOCSpdy9sh_k",
        "outputId": "86cdbbff-a524-49f7-8031-80ab3247529a"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Normal Q-Q Plot”"
            ],
            "image/png": 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NIxH/q+O3BIO1mZOSrMwwWFgJAgvpQN\nKHj9gLx+qvO9gDM/Tx0b7uGCQkBIEF+eTdmgnV7duLTivI+Twz9cUAgICeLL0Et8p/9IFff8\ntzzXGL5ZhATxpe0j/oVGz/gXXqjT4YJCQEgQX7rN8Z16M17xLTzjuI/BzSIkiC9TT/Cdfin8\nrZ0+Kj3M4mYREsSXX50Pqic7252lfXu3tIjJzSIkiDPPuU+e/fgVWd32qN/Mcb3E5lYREsSb\nX6Yc12LIfHV3Bu9V7tdrvXp4EBLELe9lSctY3RZCgnhVOi6t7nf+UBASxKniMzO+ZnhrCAni\nUtHw+j8xvDmEBPHjSOVxtw6eUvA7y5tGSBAniu9sJYktbvW96+jf4xuvZ3vrCAniwpETc+/7\n34oHG/ZU34C0p/sxm9nePEKC+HBbnnakre2F1ypf2nXayfjmERLEvs3vLP66kX+Xuidyyv5q\n0TXywwWFgJAglhV//+rKbWPE5AKB7vad8yt907TvfvYrQkgQuxZkUT2Scj7zyptIekE7ay3l\nnnq4lh+LAEKCGPX7kzee7n5wjzwvMfUK5duGw+qru9fJt4jGDhcUAkKCmFQ8UWzSWxDO2i8P\nmvqR+IMs39zQqX5+2DLpGGOHCwq1PoQEsejCvM/lh5t913KQ3G6e3PMmWT50vHT+yu+uFrP/\nNWV9CAli0U/CV7J81VD5d9eynrfLE8YqZx32ZBMJnU26ZyEkiEV3d1C+3HiSLA+4anpX79kX\nK999LG59wcPgMCfVQ0gQi64apnx5O2GXPHH0X0nT1Y+d2NB83PPOW0xbIUKCWHRHD+VLSdsh\nh4dNld90Oi+/a0xS/3nS/eatECFBLPpSUj9E7PfCfOcl1x6TPWlYz/EvPOJ43MQVIiSIPa8M\nbOBMvOmoLP9WmHbMgFm71PPmOBabuUqEBLHGO8U95flnmlD6hQMSu2/xnznL9bKpK0VIEGuW\nJHypfPUuST/m2tf9x8b3Xul+w9yVIiSILUtPcbp73q/uvfB8SpH/PO/UpA9NXi1CghjyxT1t\nnaPcN96c3eeQLO+kn33nll6Q/qXZa0ZIEDN2D3A0kVoI4tvylsZXyPK/9J12dvHIet+Yvm6E\nBDHhr3ff/7hN/qvHXS1/5+zoe1r3iWOveknRsFyWhwsKASFBDFjbhxJEolwS5sryVPpI3kGr\nj/Y9Xb3oYP+CdRZMgJAg+v2ZPfiTvIFDMhv+KLq/lQ8nZb7wCy3o02CjctHenk3+tGIEhATR\n7+wTSi/tVHzuxK4XtenYR5ZP65xM5DhD/fyj3d1ab6n1x1lASBD1ijzvyHlPyJcNXZJ+Z5aw\nS+48+0jX/trbYbe167zLmhkQEkS9jbShVPhcfivhfdralea8J87rlfeXesFfLbrttmgGhARR\nbyf9JCe9IZf1aikUraYEIudZ2jHs/mxyAvvDBYWAkCD6NbtLHjhOlncVCj07ucSBK31HZViT\nd5oJhwsKASFB9FuQ8uXH0iL5Q8/1k5wjvvKf+V3WsKIaf4ophARR772z0oWG3aVMsedp0jSv\n/8xv6o0usXAGhATRrXjzcGnAg1e2FFPbHdfv8uXlZ3+aMqnM0jEQEkStr+/tkSsSZTozHpPX\nZN8RcMn/JVzqDfljZkBIEKW239VQkBIdQmpn54yH3fPlBfUrH4LecJt2uKAQEBJEpyVJ7no5\nCU73QjpvmfTRYyn/rqcNFZc5brV6HIQEUWm5Y1TGd8K3PYTXyLnjnLOPpr28jX71X/Yf6QHL\n50FIEJX6n3/WhLeS5T49OzdKXvLoMXLHBz5wHfRd9IjjCevnQUgQjUod7/e99fV0efBomuqe\nvbCFXPj4CWf4Lprj+C+HgRASRKM99MOIS9fSb7Mb0ypH48GDvqLjc3xvl7jZ9QqPgRASRKOy\nhHtHZ/zYc/jONOFN8UQSBBr4h3q+94rE97kMhJAgGr2XQE1E6p5+cheHVN9TkNB+o3Z26YSk\nj/gMhJAg+pReJ2ZKXd5u4khIJaLEphOWlPrOPz99BaeREBJEnQMniq3vH+MSWrYQHKOX7q04\nv/iMnB94zYSQIOpcUEifeOUjYxxXX3BswNmHBub+zG0mhATR5l3l6RzVu6NE7jnttfTKsw+e\nXGjF4YJCQEgQZT53OhfR6sezzpbv6v5UfsXZe49r9TfHqRASRJeylic3KkpdJP/seXV+m6Hn\nlp+9o0Mbaw4XFAJCgujyplBA+a3SVsnjRl7W2vGd/9xtbbtYdLigEBASRJP1JxGJlDdKkIaf\nWk9yPec/e2Pz3vu4zoWQIJpsqJ+TlXX4DiFjoTg0T8wv37iwNv9Eyw4XFAJCgujxV4FERKf8\n9aKTPKLQqvxB6Je8wdYdLigEhATRomiKQKnkzkvNXvd45sVpUvkfX1dlnX2U62AqhATR4pz0\nRHo24YXUegnN51JXmu8/e3mapYcLCgEhQZT43NFxCn1Iv/6f41xKopZd/Gd/knKxpYcLCgEh\nQZS4un/W0oYP9TzD2/IBaXTb1Cd9577tmWHt4YJCQEgQJUadk9rvxJTn0wYfN1VwZpzq29/7\nRafVhwsKASFBdPB2FJKbn+IS+rchIvcNvqMRP+ecy3mscggJosNcT8oS1/IDfVz5QsLx/mdz\nj0kP8h2qEreQ9myo4UKEBDqHkwcnZ7VzXr60INXd3v+hR/dIT/IdKoC1If04qLD3fN+T25k1\n3QpCAp1LKbtrqltIdpE4/ZDvrDmOZ/jOFMjSkL5wU6KTTtijLiMkCN/RM0kc2snRaqCzy6QC\n/3k3uV/jOlMwS0Ma7HzNW3S/s5t6ID+EBOGbktBGOiD/0bX7UymzumnneKclfsB5qCCWhpQ/\nVv36kWtQaXUhHdhT4X6EBAF+FxwiZVy9f3vqIiq8ST2ndHzyx7ynCmJpSM6btZOn6fJqQvpD\noAC8d+YFGylpJybeNdOZ2+afc84VM9UtDSVjM76q9ccsZWlIjYb5Tq+je6p5RPp5ZYXr8YgE\nlR5O6Nb+bnmOy5mfJ9HbyhnFp9f/kfdQOpaGdLkwT9tN13sBXXEZXiNBmDoMbnFzs4Py5qmO\n9vmtle8PDWiwmvdMepaG9E8B9dcWvJcrz95quCJCgkpe5yLhqaZ91si7yC0tU15Mn9T4D94z\nVWHt35F2TbnCv/RKM4QE4fE62imvn5Mou4Acb8jynh6tNvEeqSrsIgT2tu+efOXpi1PIFbMd\novKMbkf7Nlt5z1QNhAR2Vnqj+uZyynI3TO0jNBgvy1uP7fIP76Gqg5DAzi50OgXnN+2Els5j\nj03I/Efe0KwP58MFhYCQwMbmk5CWmeCcc76gvErqMEBe2+gkm94zEBLY1w+SixI7tXvBtbjZ\nyObuM4b90mDIEd4zhYCQwLYelkgk8tAzd+YPHtLA1fyizFH8DxcUAkICm/KeJ5Azm45N8Igf\nUNeTjhWcyWNtcLigEBAS2FLpTDcRiYKY6hQdWeRISRLcl9jhcEEhICSwo2XJ6lZvSXILQrJU\n4CESXK5reA9VE4QENvSxJCWldRCzPB639nckcp9gl8MFhYCQwIbyBXIIAr0p5jalBI9LuPsZ\nx328Z6oZQgL7mas8BB1znuRocrGTKFEQBj0qPcx7plogJLCd9U7t2VzTlnR8OpEo5c2SFvGe\nqTYICezmaxeR1NBDrkyXqO7R0GaG6yXeM9UKIYHNPC0qD0cOEtNEoa9LJGHm1e7Xec9UO4QE\n9vKwIHhyhrsEp7q1gSj5hcuSbHW4oBAQEtjKb5LU7DhacYakbfb2PF40Lq3u91AOEBLYyg05\neQ2bnth22xKHO9Ht2FR8ZsbXvEcKC0ICO/mPW/v7q5Q0qTDTIUwsGlH/J94jhQchgX18k67u\nX0eSKEpdEp1C8sZTCn7nPVOYEBLYRek49cFIoCQSJY9HJOfLxzdez3uocCEksIvxAjk8zSTJ\nVU97epfzbfdjNvOeKWwICWzideVZncOdnioQOZwCtfirfcedvGcKH0ICW/hjjPpXI8np6peV\nJJDgSLujRVdbHi4oBIQENvBIku+zEwTBnZLVNT/NIQqN+trzcEEhICTg7xRtk7dT+zyS5HYN\nE8ntcZ96mPdUdYKQgLsLlUcicmUpr5FE5UFJVHoSHAPterigEBAS8Pa09qxOlOoJ2tZv5b8G\nSWfb9nBBISAk4Gy+b18G9eAMvs+aG/5Z6kQbH+akeggJuCod7n8YEh1CjlNdHPBuwpSo6wgh\nAVefu7VtdSRIDsEjqkU1ed1j78OcVA8hAUe3qhk5fHsGaW8/ovbPOm/hPVUkEBLw87C6i6oo\nqhvrfKSbF0r3854qIggJuNnuoMQEEt25gi+l7AeL5kvzeE8VGYQE3NwhkkN0ZOa4fJsbesvy\nHMdi3kNFCCEBNycTOTI9kqjuXEfUslie43qZ90yRQkjAyxfaYRkEtyipx7Hr7vVe6X6D90wR\nQ0jAR+nI8v0YtM0M58jeqUnLeA8VOYQEfIxQd60TyXeMfMeLcukF6V/ynskAhARcvK88Erny\nUjK1B6R0r1w8st43vGcyAiEBD7tcvrcfacckFi6Xi4blRsnhgkJASMDBK74XRmKapzMlCPTl\nwf5Rc7igEBASWO9TpSPRIwokudXDfOfu7dnkT94zGYSQwHIl6b7Ho1TflgZhcffWW3jPZBRC\nAstdodYjqW+G1Uo6t12nXbxHMgwhgdW+UD9FrKv/XXzknNOi227eIxmHkMBiZfXJobw6ujpd\n+1us46cmJ+znPRIDCAks9j/13bAJknDqseobka7POy26DhcUAkICi51PlJ3lSfHtGzQpe2gR\n74GYQEhgsYau1FMc9XzHaXi73rklvOdhAyGBtQ6rCaX6tjTckDIp+g5zUj2EBNba7fvbUb6U\nSi0SLvXyHocVhASW2pNa8c4JwR2NhwsKASGBlYrSyNH4pkbaDqvCrbynYQghgZXGEA3N6rbi\nfaco0Em8h2EJIYGFit3KszoXkUMikh7gPQ1LCAms899c37uQmkmdlNOveY/DEkICqzxUcRxI\nTwoJlMt7HqYQEljkEgqgPMNbznsgphASWGOZFlBWYnlKUXmE79AQElijmfZevgzR7etoPO95\nGENIYIm9/qPkd/H4FtbzHogxhASWOEn92BaRBEl7Zyy14j0PawgJrLDF/3ZYp29Dg/Ab74FY\nQ0hghR6Bm+xIiNpj5YeEkMACk4g8lR8nlv8r73nYQ0hgvs/VfFz+43zPPcp7HDMgJDBflm9/\nBtElCNSC9zDmQEhgtl3J5TszqFbzHsccCAlM9pu6wZu0F0jKl2ze45gEIYG5vPW1B6LWvk0N\nwu285zEJQgJzTfVvqnM71ed22Qd5z2MShASmuld7RuffL4gStvKexywICcy0xf+BExm+kz28\n5zENQgIz3axuaBBIEl3qE7uLeI9jHoQEZmrgf04nqcf57hQzR7GrCiGBiVarR69T9/tWjeU9\njZkQEpjoWDWgJN/fYs/gPYypEBKY5wb/zt65yQIlxOqGbx+EBKa5OPCdEzt4T2MuhAQmeTLF\nv4ud9sRuMO9xTIaQwBTfJFQeecsTu/uqVkBIYIKyGb6IxPK9vpvwnshsCAnYe7PizbAu/+kK\n3iOZDSEBa0fbBW5k0B6Q6vGeyXQICRg7EPDqqNzHvIcynfGQSpX/ir76rq57f/yzroYLEVL0\n8mZTFU/wHsp8RkMqnXKmLG9oStS7jnf9mTU9riGk6HV9lYwcf/GeyQJGQ5pNV8nyIGHyFHF2\n3W4EIcWkTalVOko6wnsoKxgNqe0ZsrxZmCDL4zvW7UYQUgxak1glIzrpMO+pLGE0pOTHZPlJ\n+lCW56fX/oNdAuTqQzp075wKpyOkaHR+1YzG7+U9lEWMhpSihHRuUrEsP5JU+w+KoruCpA9p\n66n9K7Sm/XWeCng7rkpGWbH2mROhGX5qN1renny6sjAxjM8XmJlSuakOT+1iTEmKPqOELbxn\nspDRkO6innn0qSz/1zWj9h882qlrxeFqEVJs+VvUd9SJ90iWMhrSkXEJaQ8rpw3ahXNcizUJ\n08sXEVJMOerUd+SMi411FVjt2bCiJKwf3be7fOnTmjaXI6RoM6TK66PPeY9kLQYh7V/NfMsM\nQooyh/UZuX/nPZLFDIf0aReid2V56IfMRpIRUtQ5PjgjYS7vgSxnNKSvXSkDlZB25rpWshsK\nIUWZ/wR3dBvveTgwGtLggk3b1EekHQXD2Q2FkKLLi0EZ5cTw0etCMxpS5mxZC0m+K4PZTAgp\nuiwI6qgv73H4MBqS41l/SIuczGZCSNHE2yKoo+t4z8OJ0ZAa3eAP6cJCViPJCCmKFAX/AcnN\nex5ejIY0KWOVGtKe62kKu6EQUtR4X7fZexHvgXgxGtK2fEdn6tjRTQXb2Q2FkKKFbrM3hfEW\ngBhl+O9IOyZnKv+AWZOZHkgTIUWFI/r9VIV/eY/EDYM9G7zb17F8NFIhpKiQpd+f4Q/eE/Fj\nJKRNwRhOhZCiQNX9vV/hPRJHRkLS/TMynAoh2d9r+ozoBt4j8WQkpFHBGE6FkGzvZ31Gjl94\nj8QVDhAJkSjSP6+L9U+bqI2RkLbtUf6rxHAqhGR3+u3eC3gPxJuh10gDg14nMZwKIdncId1m\n77rfiWKNoddIs4NeJzGcCiHZXFrwy6P4eld5tfAaCeqsLPgPseLPvAeyAaMhLS8/CMPXLzOZ\nxwch2dkhKaij9Hg4tHetjIZEr/kX7sX7keLEaiGoo294z2MPhkJa9+67dPO7mle7JzKcCiHZ\n13fB2xlm8Z7HJgyFNDvwX/RMhlMhJNt6Nrgjifc8dmHsqd3WN+i82Zp7Xj5aw0/UFUKyqXeD\nXx4RPcR7IrswfPATUz5lFyHZ06W6jKgt74lsA5u/IWwf6DvK5z2RfRgNybt0SMdjfdgNhZDs\nSf/psCx/5dHOaEhziRLTfNgNhZBsabCuo6G8B7ITw0cRGmjGZ0khJBuaqOvodt4D2YrRkJxf\nsZulEkKyn1t1Hb3AeyB7MfyIhK128WGxrqPFvAeyGaMhzWB5OLsKCMlu+gRn5GB60KhYYDSk\nAwNHv7dmnYbdUAjJbnSfs3wK73nsx/BOq5XYDYWQbGZccEdSeB/PGFeMhnTuBRPKsRsKIdlK\naYLu9ZEpG5iiHLM9Gw7imA0x6pB+/7qNvCeyI2YhPdfA8CyVEJKNNNF1tJn3QLZkOKRd866e\npri4YQqzmRCSjRQ1xvO6cOiYwLsAACAASURBVBgNaUP5/leOW9kNhZBs4y1dRjSb90Q2ZTSk\nMSmPfERPvHdtw/fYzYSQbOMLfUcv8Z7IroyGVHCtfIRWyPL39b5gNxRCsgv98VRZblGKLYb3\ntVuo3MRnysJN/ZjNhJDs4gRdR//lPZB9GQ2p3u2ynLxIWXgeb6OIOf8NzsjxG++BbMxoSMMb\nfiL37Krc7SfmsBsKIdnCZcEdJfOex9aMhvS1p4v8FOWf3pHGsBsKIdnAJP12ht21/0wcM/x3\npJULZO91CSQM28VsJoRkAxn6jlbznsje2OzZcGTDYRbDVEBIvKXqMqp/iPdENoejCEFV3kxd\nRy15T2R7RkPqV6EPu6EQEmfd9c/rcJz82jB7P1JKHruhEBJfc/Udfcp7IvszGlKJ5tDq6X33\nsRsKIXG1Td/RdbwnigLMXiNde4nhWSohJI5K9e8/YvmHjZjFLKQVeGoXG27UZSTifRPhYBbS\nB/h8pJjQKTgj4UXeA0UJoyHt9dn5SUcc+zsW6PZnYPn/jrGN3VGEnmE3FELi5WBwRxLLD72K\nbYY/H8lnxOQP2c2EkHg5FPzxsLSH90DRA3s2QIUJuu0Mr/MeKIogJCjXQddRLu+BoonRkMo+\nv/vKK+/5wstuIhVC4qCRriMc37suDIb0dnPfP3rL9xnOhJA48Lp1HTXEr6AujIX0lCD0m/vS\n0ntPk0T1Yz4e6stoKoRktYG6jOgg74mijKGQNroy/bszfpvn+UOW73IxmgohWUz/tgl6jfdE\n0cZQSFfSsvLFb8VpcmnXeoymQkjWGqTv6HjeE0UdQyG17VR55knHvN+LLmMyE0Ky2NP6jlrz\nnij6GAop5aLKM2cq//6DWb0fGSFZqEz/qS10E++RopChkFwBj0C30FnvMJlIhZCsU6w/mqrA\n+G8Z8cFQSHnDK8+8IJ3JPD4IyTpJuo6kMt4TRSVDIQ1P3Vu+uD/rOEYTqRCSVRbon9Yl4vEo\nIoZCWkrn+v/Zy0bTQ8xmQkiW6avvqCPviaKVoZC8J9KJn5QoN/Le8dShmOFUCMkazfQd/cF7\noqhlbM+G3ScTeRoXuoh6bmc5FUKyxEn6jq7iPVH0MrivXdnSIVkCZQ1+ge0rVIRkhYX6jnry\nniiKMXgbRUkJo1kqISQLfK7v6D7eE0UzvB8pThU10GWUynui6IaQ4lNxMv58xBRCik8TdR2l\nl/KeKMohpLj0tq6j5bwHinoIKR6NCc5IOMJ7oOiHkOJQQ93j0WbeA8UABiHtX723+utFDiGZ\nSf9pfGyPtxGnDIf0aReid2V5KA4QGSXKPLqOHuE9UUww/KnmrpSBSkg7c10r2Q2FkMxzm/7P\nsOt4TxQbDB+yuGDTNvURaUfB8JDXrzuEZJKSNH1Hdf/1Q3WMhpQ5W9ZCku/KYDYTQjKNU99R\nL94TxQqjITme9Ye0yBnWz3rXL3v11Y/+ruVaCMkc+t0ZqDvviWKG0ZAa3eAP6cLCMH5yz9U5\nvl9gwW2Ha7oeQjLF8fqOmG4him9GQ5qUsUoNac/1NKX2H9zahFqMm3XPPTeem0cdavrIEIRk\nhjt1GYmsDvoExkPalu/oTB07uqkgjHf2TXAu9S+Vzhem1XBFhGSCv3QdObGbKkOG/460Y7J6\nuNusyeF8dEHu+MrlUfk1XBEhsVes+xAxVoeXBg2DPRu829eF+T5z552Vy7fof5EbcjMqJNL+\nOk8FNWsZ3FFz3vPEGCMhbQpW+w8Wnl25PLyx7sLS15dWmIhHJNbOCspI+Iz3PLHGSEi659y1\n/+A0YW6Rb+ngzTSzhiviqR1rTYJ+VR7e48QeIyGNClb7D+7tTCn9xk299IITE6lPTakgJMY6\nBm+u4z1ODLL2bRTF93eUtA1Gxy2s8R2ZCImtE4OfO/zGe54YxCCkrd99/OPOsH/4yO+rVq2r\n7WCSCIkp3fv43uI9TywyHNLCxtov55jnmY0kIySmjug+tuVE3gPFJKMhLSB3/wumjOku0H/Z\nDYWQ2LlE9+cjknhPFJuMhtRy4L/a6Z/N2zCaSIWQGLmYqtjCe6bYZDQk1xf+hfluJvP4ICQ2\n2lft6FPeM8UooyFlr/AvPNaQyTz+G0NILPSokpFQxHumWGU0pPHX+xeGXMFkHh+ExMKxVR+P\nwtkjEiJhNKSt3Ue/+etfa14e1H9deLsJhQUhMXB61Y7+5T1T7DIaku43xWgqhGTcjqodfcB7\nphhmNKQRdd1NKCwIybimVV4f4XhBJsKRVmPUFfqOBvOeKLYhpNg0VJdRYxze21yGQyr938vP\n+zCbCSEZlhuc0Zu854l9RkNa2Zj1hgYVQjLk/uDdggT8Y5rPaEjHpU9b8LgPu6EQkhGz9K+O\n8KzOAkZDSnqN3SyVEFLEvFUOSjyG90hxwWhI9Vexm6USQorUQUnfEd4OawmjIV12HbtZKiGk\nSFXpiH7lPVJ8MBrSoaFnPfvxcg27oRBSpBKrdPR/vEeKE4Y/HykfW+1soyypSkes9n6EWhgN\nqbvn7Btm+TCbCSFFqECfkYDDnFjFaEieZ9jNUgkhRWKiviOWb1qGmhn+oLHv2c1SCSFFYLL+\n4ehn3hPFE6MhXXQ7u1kqIaS6G6vL6HXeA8UXoyHt7T9l2Zp1GnZDIaS6uy+4o9a854k3DN/Y\nx24ohFRnu4I70n9CAZjNaEjnXjChHLuhEFJdlYpBHaXxnif+MHs/0sFthmephJDqyBPUkYP3\nOHGIWUjPNTA8SyWEVCc/6LbXbeQ9UBwyHNKueVdPU1zcMIXZTAipbp7TdbSS90DxyGhIG7LL\nn07cym4ohFQXuu0Mwt+8B4pLRkMak/LIR/TEe9c2fI/dTAipTrKDQ0JHXBgNqeBa+QitkOXv\n630R8vp1h5DCd05wR2N5zxOnjIbkXKjchPrJvjf1YzYTQqqDpcEdNeM9T7wyGlK922U5eZGy\n8DzLv10gpLA5gzrK4j1O3DIa0vCGn8g9uyp3+4k57IZCSOF6J/gPsQk1fjIvmMjwG/s8XeSn\nKP/0jkyPsYGQwqPbUbUF73nimOG/I61cIHuvSyBh2C5mMyGkMA0O7uha3vPEMzZ7NhzZcJjF\nMBUQUhjKMoM7SuI9UFwzGlKZ+mXny4v/YjWQBiHVbk/wyyOivbwnimvGQvqs44fK1w9SiRwP\nMxwKIYXBqevofd4DxTdDIa1KpGdk+UCWZ/rteSLLPbwQUq0G6jpiuasj1J2hkM51vKN8/Q/N\nk+XfnHg/kpX26zoSNvOeKM4ZCqlwmPp1uEv9aNLBLdkNhZBqs1rXkYQXSJwZCsk9S/nirddX\nXb4qkdlMCKk2X+o6msh7IDAW0r2y+n+O2uG/Z7F8WyZCqtG3uqd1+NwW/ow9tZuhfHnId3jp\nSzLZDYWQavR4cEfuEt4DgcGQBjctlY+2S1L/GFua35vhVAipBh2DO8IBg2zBUEhL6cRHhtLl\nylLZdJrLcCqEFJpufwbBy3sgUBkKqexM5TfZZb+s7vXVnOVdHyGFckC/PwPL//+CyBnbs8H7\n8SNvaM/QLz6V6eeHIKQQrtNlRMfxngh8GB2Oi/H7YBBS9W7Td4Q3ltsFs+PaMYWQqvWvvqNP\neE8E5RBS9Phd0HX0KO+JoAJCihr646nSBbwngkoIKVoc1D0eCYt4TwQBEFKUOKrb7p2Jvx/Z\nCkKKEjnY7G1rCCk6XBbc0WLe84AOQooK7wV39CrveUAPIUWD34I7Op73PFAFQooCU4I7Yrmf\nPTCCkGxvnyu4o+m8B4JqICS726j7+9HZvAeC6iAku3MHd9SI9zxQLYRkcy2COxL38R4IqoWQ\n7K1ZcEe0m/dAUD2EZGvjdR29w3sgCAEh2dkTuo6m8R4IQkFINrZM19EzvAeCkBCSfR0J3uG7\nfhHvgSA0hGRfI4I6OpX3OFAThGRbtwR1hI9tsTeEZFfnB3Xkxvv47A0h2ZT/jRP+l0kiju9t\ncwjJnkrL97DznX7Oex6oBUKypdLkoCd2df8dgcUQki2drvVT/nnLo3mPA7VCSHZ02P/ETtBe\nIgn4XEv7Q0h21Cboid01vMeB2iEkG1oe1BHLj4sHsyAk+zkqBWQkbOU9DoSDW0j/rKvhwvgO\nKS/w8QgfJBYduIU0s6ZbieuQrgn8C1Ib3tNAeBCS3RwM+Dss0Q7e40B4EJLNeP1/PPJoW76v\n4j0OhMnSkLoEyEVI1Xk/aINdGu9xIFyWhiSK7goSQqrGyKCO6Eve80C4LA1pZkrlpjo8tauq\nODe4o8G8B4KwWRrS0U5dj5YvI6QqvM0CNzMQteI9EITP2o0NaxIqDlxdJaSSV5dWmBiXId0c\nuN2byMl7HqgDi7fa7as4wOGns3UXbWzRtEJWPIb0SPDzOvqJ90BQB9hFyC70HZ3IeyCoC4Rk\nEyt0HeWV8Z4I6oJHSHN71XaN+Atpla6jobwHgrrhEdLFtd5A3IX0UnBGDryVL9ogJDuYENwR\ndmiIPgjJBoZXJKRt+RbW8h4I6gwh8Xer7vXRa7wHgrrjEdLeTbVdI55C2ndCcEbCD7wngghg\n8zdnL+o+a5mW854IIoGQ+PpCqHxtpLmL90QQEYTEU0l73cMRXcJ7JIgMQuLoHVHf0W28R4II\nISR+VupfHolf8B4JIoWQuClL1HXkwGcgRS+ExM2ZwVsZSPib90QQOYTESUkr3eORsJr3SGAA\nQuLjUf3ro6xtvEcCIxASD3uzAh+K1C/zeY8ExiAkDv6QdA9H4ie8RwKDEJL1SpL8j0TlT+9G\nH639h8DeEJL1rtTqkYTyzyzHX2FjAEKyXprvcShF9D0iNeE9DzCAkCz3RPkrI98fZD0x/D81\njiAkq10WvJ2hHj64JSYgJIst0LbSlW9nEO7lPQ+wgZCs9XbQw1GLIt7zACMIyUpHjgvq6Eze\n8wAzCMlKXbU/HzVw+EN6ifc8wAxCstAD/hdGZ4mioLxIch3iPRAwg5Cs83rFczq3tq3hft4D\nATsIyTJvqvWInor9VK/kPRAwhJCsssR/gAaP/7hBq3gPBCwhJIss9HckChna0iLeAwFTCMka\n89V9VKn8P6IJvAcCthCSJe7yPR4lOP0PSy/zHggYQ0hWqPjYFiFfLUr4g/dAwBpCMl9pS19E\nvid2SknzeE8EzCEksx0ZUP5wJPn3VMXroxiEkMxVdFbFszr/+2EpBx+zHIMQkqn2ZVRkVH7i\n3Mx7KDABQjLTweSgvb3VmqRaP2UNohFCMtGhVP/fYCuf10nbeQ8FpkBI5vnFXf5AJJQ/Hjm+\n5D0UmAMhmeYXZ3lHkuB/idTuL95DgUkQklkWC74/HQmS8oROy6heCe+ZwDQIySTfqC+KMhq7\nhIotdiPwPr4YhpBM0l/buiA0KN/pe+wu3hOBmRCSOa4u/9tRgdbRQ7znAZMhJFPcL6ovkJwO\nwffy6EPe84DZEJIJ9k3WHoacgu9AkMJ/eQ8EpkNI7K1Vj5LvFkj0H1D1c94DgfkQEnP/qh9/\n5M4WlZISlZyEpbwHAgsgJNaONtSe12WN822vE+7kPRBYASGx9dNJ2rM5iahBp6ZJIolJ+3iP\nBFZASCwdGeHfK8ih/NcyJ1P5upj3TGAJhMTScPVQxAkJgiQm+XZncDzLeySwBkJi6FMxQXko\ncrgqjrqVhN0Z4gVCYuhS3/smciT/GyfS8Sa+uIGQGEpX9/V2DxdyfJ/bcgn29o4fCImRfZNT\nyo9xcoHvAWkZ75HAQgiJjcWOijfBCpSiLjzCeySwEkJiYpb2aJQrOgXtEA1EiXX/Z4VohpBY\neEbJRxQThTH+N/E5phfzHgmshZAY+DfZmeuSGnSXnD0Kkl3uRPEj3hOB1RASA08nZkticmrT\nUz2dWzQpyHEU8h4ILIeQjPP2938I38J8wZnoIOF93hOB5RCScdcKAiUmJ5Eg9vIIJDjO4z0Q\nWA8hGfax8mCUIJG2xU49zMlUbGiIQwjJqKOZQlL9UXn1fEdTzbvjH94DAQ8IyaCiM30Hfzy5\ngSBRd97TAC8IyZBdp2rvg02SUkUSUvJu5D0P8IKQjLhDzcjtohZZzi59WzgkHOYkbiEkA6YI\nArnqd6AUoaB7K3I6BvEeCLhBSBHadlUD3+YFMfNCwaG+t5x67ec9FHCDkCLzVqIoah/WImYL\nx6Xnq+/o68F7JuAIIUXkN09yQUGyUI9EKaGX5MrOdJKwhfdQwBFCisjENmliunBMYpLoFgqo\nUXpiSsIY3jMBTwgpIq0GdCfq3TSvD0kpJEiCILTczXsm4AkhRSR3WCHVn512jlP0fcqy48LD\nvEcCrhBSRLo2Jalli9cSOmi7NTRbgt3r4h1CioS3kIQMl5C6pL1EJMznPQ7wh5AiUNqL6rWW\nGiQ4tIOdLOA9DtgAQqqj0u8fuKQR5XbNJO1zlhvN3M57IrADhFQnRdclkP/TlR1Cj6dva897\nILAJhFQXZafVkxp6yEldsuq1T8y55Plc3hOBTSCkupjncrtJ7JZKx7YeJR0/QLyhLe+JwCa4\nhbRnQw0X2jSkn1zJlOwmxynpNP3YwgnZhQVX8B4JbMLakH4cVNh7fqm2OLOmW7FlSEXznOrx\nH5tTo8S7hZEZfcYLOQnYvw58LA3pCzclOumEPepytIV0ZFYSkVOglkk0KPERh+BMaSQ4ruc9\nFdiFpSENdr7mLbrf2e2gHG0hrTzNQaLbQwkeMUVq6+ovdmtL+a3FDbznAruwNKT8serXj1yD\nSqMoJO/ax2e2EAR3I0oQGlM3p7u+kORo4c5v48q6lPdsYBuWhuS8WTt5mi6PmpB2X6T94UgS\nRIeQKg46nQrI6fs7kiRcdJT3dGAblobUaJjv9Dq6J0pC2tXymORTEwoTPSNoABUm0I9Cb/WF\nUv1m7frd8xPv4cBGLA3pcmGe9n/i3gvoisuiIqSL213c7aqu3WZJw5THJHEunZn4IHWQbuA9\nFtiOpSH9U0D9tQXv5cqTI92FW3p1qVBA9jiOyC53a6lR9rR2DzdMkuhMcVFmlroBfJqX91xg\nO9b+HWnXlPK/YL7STH8rh++bU+F0ezwibSygaYkTkpzdLzqZzqZx7iRhoFsQb+c9FtgQdhEK\nqWTdcT3o12aPDujtcko0hBKEdJGEzp/xngvsCCGF8ONAt/Ye8sLOC7IaCe6sTKG+QOLwv3jP\nBfbEI6S5vWq7BveQ/rnB0apNQsZkR0I34cx8apig7h2Udj32CIIQeIR0ca03wDukZ1OkgnZC\nUjP5LSG9UCQHCYKY/h+uI4G9IaQqvE93JI/w4KCLRtC38oDeDcjpybloznIcJghqgJD0Ss9J\nzjl1QlZa0mOH3W3kmwrciXMd+JRyqAVC0ns4/TP6bkHrddIweQZd1lZ6wZ08ntswEC14hLR3\nU23X4BlSqztX084vpG2dE7xfUZr6B9hrS7kNA9ECm791DtFX2+mHsvZnLqIlSx1J0sKOg3mN\nAlEEIenspe/lDlfJP2d1IMktiiNbNMc2b6gdQtLLeUp+yzG/bHN/kcjhaDvzX26TQBRBSHpX\ntfxXfjKxYFiKKD4ll3EbA6ILQtLZvTArZ+bGX6ZmS/V/5TUDRB+EFOzplPonNSAiZ3q7nZxG\ngGiEkIK87XigVJb/HZ1Q2BUfHAZ1gJACbSs8YelG5XR9Qo493lkI0QIhVSq9xkltssRJh39t\n2CGTw/ohiiGkChuGpd5G/8qfFJySPfRDwt4MUBcIye/7bkQOgZbL8vPUv+SFDKvXD9ENIfn8\nlDpqZpuSLz319n6W0vBqefDZFq8fohxCUpQuPMWddPrIIbL8rNA1YcqkUTM9P1u5foh+CEmW\njwxIv0S4fpyUpyz3pvSzGiRmvWvh6iEWICRZvqbRhlW0X36IFsjPO8QFE9yX7LNw7RATEJJc\nlPqM/Cttkb0NU+6VJiT/O6ANjukNdYWQ5NW0Qy7JXKi+QKLOHepntl5v3bohViAkWX1aJ9+W\n/bN8EU0+TRi0qMi6VUPMQEjyHmm5LJec4+kgpg6VZlu3XoglCEmWh/QvlWXvUMnRaOJXFq4W\nYglCkuV1WQO+OHCep6DTQQtXCrEFISn+OFUgck7Em8ohYghJVTws48ViS9cIMQYhKQ6dmotd\ngsCQ+A6pZHPZzlsGtMpK/96S1UHsis+QDt7RJ6f1mAW93eR2FV7RJK1h43Wmrg9iXlyGtL11\nwaylCzpR32U/ZDV2tGi95dCgdngjHxgRlyEN6rFPljcljHX8/GT2nzmOP2R5p+cdM1cIMS9+\nQtqnPeYceuOu2QvpO2XpnlbefpMnDm3eNWux8t0JNzNfIcSTOAlpy/g88vRYKr9bP+X44zzi\nx8pZ4y6Q53QfnnLC/tOuUb4bcjXbFUKciY+Q1uZ0f/q7D6a7LnDPPCzLj6ck/CjLF54vP9gq\nJeOwfOpM5RpNH2G6Qog38RFSz8El6skyob968qV06lBZvq952TD3CeInRZnPyvILrr+ZrhDi\nTVyE9DP5tm4fEk5RT8qaD3GXyluTzxP6lFyeflrO/r0PJmCvbzAkLkJ6Idd3upHaaKefuOij\n4i3DKPmV75ceQ0IWZS1guTqIQ3ER0vMNfKf7hBa+hXkCKdoMTKfM07/+9pXv8F4+MCguQvpR\n+NO3UK+l73T8ibtnu9SNdTjKCbARFyHJ3UZof0T6TJT+45Vl74OOT59z3MZ0DRDn4iOk1Zl9\nlq75/KaEKx73tBxzbrPEZ/4jPcB0BRDv4iMkeePoeuRo/7Qsb3rgookPbX3E8STb24d4Fych\nKbZXvnNvjuNp5jcP8S1+Qqp0s+tVE28d4lL8heS9IvF9024c4lXchVQ6Pvkjs24b4le8hVR6\nXvoKk24a4lmchVR8Rs4P5twyxLf4CunQgNzVptwwxLu4CunAyYU4yAmYIrZDWvfKy2srv9t7\nXKtNTG4WQC+mQtpxy6AOZ84/Uv7t2uMpox51Kz/2444ObbYwmQ6gilgK6X9ZrWc8OCWn7Vbf\nt3/lDPlNlv84o57v6dy2tl12sZsQIEgMhbQ3e5L6hvI9vfp6te/P66W9v7ys30j1ZGPz3njP\nBJgmhkJ6oNC3N92fovaXorLkl33nv+MpUp7mNTrR2uPyQ3yJoZDOnuRfaH+/+nUX+V8crae/\n5F/yBh8J8WMADMRQSIOn+xd6365+PSx84fv2O9q9MutsfFI5mCmGQpoyxHdaluN7k0Tna3zf\nzzpmeeqYEkaTAVQrhkL62OHb++eJJN/WuRfc/6eefJQwM/mSMnazAVQjhkKSz819pVjed5/7\nYf/3N0un3Xr7EGmkZ4aX5XAAVcVSSMXXeBwNKPvxijO+uvSEPpNvc85kNxhA9aIrpLKVixev\nrOFp2r+fL1mp2zr3rPNehoMBVC+qQlrVlho3prar6nBLj0oPMZoJoAbRFNLatNHbZHnb6LTf\nwr6he6Sn2E0FEFI0hXTGAG2jQdmAkeHezhzXUmYzAdQgikI66nnbt/CWJ7y/rnqnu19jOBRA\naFEU0lbyP6VbS1vDuRHv5YkfsBwKILQoCukA+Q9b8qVwMIzbKL0w7QumQwGEFkUhyZ1n+E6n\ndw7jJo6elfEVy5EAahJNIb3kO0Lqq66Xa7+FohH1f2Q8FEBo0RSSPFvqO2NGXymMj6k8dEoD\nHC4ILBRVIck/zhw0aGYYjzQHTmr8B+ORAGoSXSGFaU+PY3C4ILBULIa0vX2bsLaPAzATgyFt\nPbbLP+xGAQhH7IW0oVkfHC4IrBZzIa1tdBIOFwSWi7WQVjcYgsMFgfViLKSVmaNwuCDgILZC\n+jx1LA4XBDxwCal0zbc1P/+KMKSPkyfjcEHAhbUh/e+sDiNWyevaEqXMr+l6kYX0lgeHOQFO\nLA3pKyc5KXV9r6QxZyTTmzVcMaKQXsDhgoAbS0Ma4ny1dHO7sdJyWf4tqX8NV4wkpGcc90U6\nF4BRloaUOVb58hH1VZfHZdRwxQhCWiA9XPuVAExiaUjOWcqXg3SJuny9o4Yr1j2ku6VFEQ4F\nwIClITU5X/2adq36dVT9Gq5Y55DmuF6KdCgABiwNaYJ7efniCmdNx9SqY0jeq9yvRzoTAAuW\nhrQuQ7jOtzTW6fhGf+mPKytcX6eQvJclLYt0JAAmrP070pr+N/oW2uW/ob/sD5EAote3FoZU\nYUs15x3cU+nrlRG4OesZcz1A95u8huxJJq+gb1+TVzAp2+QV3E8PmLyGrJsjuff9UPcKzN/X\nLjKLC01ewUb60+Q1NF5k8grGjTN5BYsam7yCP2mjyWsoXGzyCsoZDWluLyZjVIGQaoeQahc1\nIV1s0kMaQqodQqodQio053YrIKTaIaTwISTTIKRaIaQKCCkkhFQrhFRhr0lHb0RItUNItYua\nkMyCkGqHkGqHkApNXgFCqh1CCh9CMg1CqhVCMt2SFiavYCttNnkNLZ8zeQWTJpm8gudamryC\nzeF98KkBLZaYvIJydg3p6F9mr2G92Sv42+yj8u3ZY/IKjv5t8grM/yX8ZdWhEe0aEkBUQUgA\nDCAkAAYQEgADCAmAAYQEwABCAmAAIQEwgJAAGEBIAAwgJAAGEBIAAwgJgAGEBMAAQgJgACEB\nMGDbkNZPbOrKGv61iWvYc3WBq/HwFSau4ei1YhfTbnzvtEJngwlmvsPU1PFlC34B5t+HKtk1\npLWZrrGzxjidX5q2ht2NafBNYxyen0xbw5rOKebdE4s708g7xzubmPcuWVPHly34BZh/Hwpg\n15BOET5Tvr5KZ5u2hktpnvL1FRpk1gr2JXRd5zbtnng/3a18fZGuNmsF5o4vW/ALMP8+FMCu\nId2ofRxgqbODaWu4op/6dn5vQqFZK9h99VHZvHtix5Qi9aR5jtekFZg7vmzBL8D8+1AAu4bk\ns5lGmLyGIqdJn0vjY9o98YjUTzsdR2YeP8TUkHxM/gVYcR/S2DmkQ5+0T6n7ZxDWzUPa8wvT\nmHZP/J18B7WbRWZ+5K4FIZn8C7DiPqSxcUhpRGPNPlzTp67eJWbevmn3xFV0qXY6l141aQ0q\n80My+RdgxX3Ix24htD+6yQAABxRJREFU7b1YMVdbvHbS8WJv9v8KAWuQl7g77zZ1BSaGNFU7\nvYdeM2kNKtNDMuUXEMCk+1A17BbSJvUzpSueNX+S1L7MvDV4b6ZT97O++eD/CabdE9fRBdrp\njfShSWtQmRySSb+AYGbch6pht5B0RtMa027bO54uKzXt1n1MuycWO07UTs8lMw9Ja25IVvwC\nZHPvQ5VsGtLm9udpp2eQea8Up9Fdpt12OfPuiT0SDylfy/LyzVqBytyQTP4FWHEfqmTTkORG\nrq+Ur78lJx8xaw2v0DSzbrqSeffEhXSL8vVRutWsFahMDcn0X4D596EAdg3pNcl5zg3jkugR\n09bQjC6bqTFrJ5tPlduWcpUv/5hx66V9aPit5wjtDplx4ypzx5ct+AWYfx8KYNeQ5K9GZEvp\n/d80bwVUboNJK5hdvoJ1ptz8gemFzoaXmrfNy+TxLfgFmH8fCmDbkACiCUICYAAhATCAkAAY\nQEgADCAkAAYQEgADCAmAAYQEwABCAmAAIQEwgJAAGEBIAAwgJAAGEBIAAwgJgAGEBMAAQgJg\nACEBMICQABhASAAMICQABhASAAMICYABhATAAEICYAAhATCAkAAYQEgADCAkAAYQEgADCAmA\nAYQEwABCss6ESD/8bhRtC3XBpsjHKb9lwzcCMkIy2dUVn+9IvSIKabb6I7MHhviY1cAGvC+N\naOhK6zDj77reMkJiASGZ6o1pikyaqnx9KJKQttK7NV0c0MDuEyl56NQJ7cn93zreMkJiASGZ\n71jyfT59BCG9EW5IZSfTudoHM7+fKfxf3W4ZIbGAkMxXGdL6OU1c+bd5leXtUwqcWcO/Uc/e\nOC7PmTn0a1m9S+/o73kj4MLB6nPC5b7XSNsm5CW2f7BEudrXIzKdhWM3yIENLKUTvL6lT4UW\nZepP7lWWS6hf0PXPpQPXFLoa3e8NvGXtRirnKbqnfWpyu3vKrPv3iQkIyXyVIV3YafY9+bRE\nlncWps185q5G7k9l+e+c5BmL72zoXi7L59Ho0+76OeDCFefRza/t1u7uOxumXXbvEJogyys9\nebctvDYl55/AkIbQJ+Wr66cEEhhSwPUvoIGXrPjfAHoq8JbVGwmY50Ia/ehjp9Ol1v87RTWE\nZL7KkHofleVVNEyWJzu+Vc74O6Wreud+VVlcIx0ny+NpgPpAEHDhbO0JmHp3n0zvy2ofq+UF\nnT9RlubRvMCQsjwl5aubS3cHhRRw/Ql0rrK4noYE3rJ6IwGrTOyp3siVI0ut+KeJHQjJfJUh\nvaZ89UpdZW9W522qgXTAm1Zfe07Wm/5RrvCceoXKCyvv7t7MfPVq6z/epd3U0SMf0dUBIZUK\njStW9xJdGfzUrvL6E+g99bvEjrqQAleZlrfDgn+TmIOQzFcZ0mr1JO1YeXvFRvFfttLJ/gu/\nVP5bqSwFXFh5d99Cp1Tc3tN909VLpwWEVEKFFRcv1YdUef0JtMY/QXBIgat8iFLPe2qz2f8m\nMQchmU+31U65G6+jju/67F1HQ7ULp9Iy/xUCLqy8u/+hPh3zuY66Lvp0xRNBIclZruLyy++l\ne4JCCrh+5QTBIQWuUv5oRBIJgzZa8A8TSxCS+aqGtJ06ll+4zf+IdCF95b9CwIWVd/eD1Nt/\n1pGE/APKyXvBIQ32PWlTnUZflId0SAkp8PqhQgpcpaJo2QVC82IZ6gAhma9qSHKWR72fyzuV\n/+o10F4j9RD2ll8h4MLKu3t25lFlae281RvodPXS64JDep56+TdYr5JaKDc4gtQfX62EFHj9\nUCEFrtJnMn1t0r9GjEJI5qsmpMl0vbK0M1d5vnaRtgnie6FfxRUCLrxH26Sn3t0voseVpXNo\n1WGhk3r9hnRxYEilPWjsfnXhu0bCu9ptfKZ8vUYJKfD6ARNU3rK21a5ilSvytD0jLqXvLPm3\niRkIyXzVhLSjgC5cfFeB8wNZ3pKbfP1/b81J+bHiCgEXvkzd7/tGu7tvynVMnTuEzlf/ZHTx\n8zdl/J+j0ZKDATslbG1HWeNuufYU0bNI/XYFdfn4q+v6pPQLun7ABJW3rN5I5SpL2romzl8w\nXuzttfqfKbohJPNVE5K8bXK+I32Y9vTp7wsbOHLOWVN5hYALj45MyHjJt2fDxrE5zqb3lSqP\nG6Oz005eLt+anLstcO+e4vu6pxIdM+0P37eL2yTUn/RvXu+g6wdMUHnL2o1UrnL3Fc0S0zrc\ndcCif5xYgZBiyVn0Ae8R4hVCiiXvUB/skMAHQoopp1GPOQ/xHiIuIaSYcvCSDFdf3kPEJYQE\nwABCAmAAIQEwgJAAGEBIAAwgJAAGEBIAAwgJgAGEBMAAQgJgACEBMICQABhASAAMICQABhAS\nAAMICYABhATAAEICYAAhATCAkAAYQEgADCAkAAYQEgADCAmAAYQEwABCAmAAIQEw8P9NpLTc\nTTg6gQAAAABJRU5ErkJggg=="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "ugarchforecast(fit_01, n.ahead = 5)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "id": "qqQR2b2dr96c",
        "outputId": "d6a8ad63-db85-4310-93ec-a45f5f049b5a"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "*------------------------------------*\n",
              "*       GARCH Model Forecast         *\n",
              "*------------------------------------*\n",
              "Model: sGARCH\n",
              "Horizon: 5\n",
              "Roll Steps: 0\n",
              "Out of Sample: 0\n",
              "\n",
              "0-roll forecast [T0=1972-09-27]:\n",
              "    Series  Sigma\n",
              "T+1      0 0.2562\n",
              "T+2      0 0.2573\n",
              "T+3      0 0.2582\n",
              "T+4      0 0.2591\n",
              "T+5      0 0.2598\n",
              "\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**O que fazer se quisermos ajustar um modelo IGARCH?**"
      ],
      "metadata": {
        "id": "J1rDSXsUNeUR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "spec <- ugarchspec(mean.model = list(armaOrder = c(0, 0), include.mean = FALSE),\n",
        "                   variance.model = list(model = 'sGARCH', garchOrder = c(1, 1)),\n",
        "                   distribution = 'norm')\n",
        "fit_02 <- ugarchfit(spec, serie_c, solver = 'hybrid')\n",
        "fit_02"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "ls-DathUNtdH",
        "outputId": "adc7059f-6c88-4716-fc3e-d81be16c9de6"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "*---------------------------------*\n",
              "*          GARCH Model Fit        *\n",
              "*---------------------------------*\n",
              "\n",
              "Conditional Variance Dynamics \t\n",
              "-----------------------------------\n",
              "GARCH Model\t: sGARCH(1,1)\n",
              "Mean Model\t: ARFIMA(0,0,0)\n",
              "Distribution\t: norm \n",
              "\n",
              "Optimal Parameters\n",
              "------------------------------------\n",
              "        Estimate  Std. Error  t value Pr(>|t|)\n",
              "omega   0.008876    0.007175   1.2370 0.216097\n",
              "alpha1  0.059739    0.027512   2.1714 0.029903\n",
              "beta1   0.813572    0.122902   6.6197 0.000000\n",
              "\n",
              "Robust Standard Errors:\n",
              "        Estimate  Std. Error  t value Pr(>|t|)\n",
              "omega   0.008876    0.007953   1.1161 0.264391\n",
              "alpha1  0.059739    0.030821   1.9382 0.052596\n",
              "beta1   0.813572    0.136827   5.9460 0.000000\n",
              "\n",
              "LogLikelihood : -80.96887 \n",
              "\n",
              "Information Criteria\n",
              "------------------------------------\n",
              "                    \n",
              "Akaike       0.16794\n",
              "Bayes        0.18266\n",
              "Shibata      0.16792\n",
              "Hannan-Quinn 0.17353\n",
              "\n",
              "Weighted Ljung-Box Test on Standardized Residuals\n",
              "------------------------------------\n",
              "                        statistic p-value\n",
              "Lag[1]                      1.325  0.2496\n",
              "Lag[2*(p+q)+(p+q)-1][2]     1.593  0.3402\n",
              "Lag[4*(p+q)+(p+q)-1][5]     2.441  0.5185\n",
              "d.o.f=0\n",
              "H0 : No serial correlation\n",
              "\n",
              "Weighted Ljung-Box Test on Standardized Squared Residuals\n",
              "------------------------------------\n",
              "                        statistic p-value\n",
              "Lag[1]                     0.9291  0.3351\n",
              "Lag[2*(p+q)+(p+q)-1][5]    3.8456  0.2740\n",
              "Lag[4*(p+q)+(p+q)-1][9]    5.7842  0.3238\n",
              "d.o.f=2\n",
              "\n",
              "Weighted ARCH LM Tests\n",
              "------------------------------------\n",
              "            Statistic Shape Scale P-Value\n",
              "ARCH Lag[3]     2.291 0.500 2.000  0.1301\n",
              "ARCH Lag[5]     4.060 1.440 1.667  0.1686\n",
              "ARCH Lag[7]     4.767 2.315 1.543  0.2491\n",
              "\n",
              "Nyblom stability test\n",
              "------------------------------------\n",
              "Joint Statistic:  0.304\n",
              "Individual Statistics:             \n",
              "omega  0.2114\n",
              "alpha1 0.2224\n",
              "beta1  0.2136\n",
              "\n",
              "Asymptotic Critical Values (10% 5% 1%)\n",
              "Joint Statistic:     \t 0.846 1.01 1.35\n",
              "Individual Statistic:\t 0.35 0.47 0.75\n",
              "\n",
              "Sign Bias Test\n",
              "------------------------------------\n",
              "                   t-value   prob sig\n",
              "Sign Bias           0.5313 0.5953    \n",
              "Negative Sign Bias  0.1315 0.8954    \n",
              "Positive Sign Bias  0.7570 0.4492    \n",
              "Joint Effect        0.5961 0.8973    \n",
              "\n",
              "\n",
              "Adjusted Pearson Goodness-of-Fit Test:\n",
              "------------------------------------\n",
              "  group statistic p-value(g-1)\n",
              "1    20     10.92       0.9265\n",
              "2    30     23.24       0.7654\n",
              "3    40     29.44       0.8663\n",
              "4    50     44.50       0.6559\n",
              "\n",
              "\n",
              "Elapsed time : 0.231209 \n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Extensões do Modelo GARCH\n",
        "\n",
        "- Os modelos GARCH capturam algumas das características frequentemente observadas em séries financeiras. Contudo, outras característica observadas nas séries não são capturadas. Para uma leitura dos chamados _fatos estilizados_, ver o artigo do [Cont (2001)](https://www.tandfonline.com/doi/pdf/10.1080/713665670) [**leiam!**]"
      ],
      "metadata": {
        "id": "S_t55TFWP4sI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Definicão: (EGARCH):** Um modelo EGARCH(1, 1) é dado por \n",
        "\n",
        "\\begin{align*}\n",
        "r_t &= \\sigma_t \\epsilon_t, \\\\\n",
        "\\log(\\sigma_t^2) &= \\omega + \\alpha \\epsilon_{t-1 + \\gamma} + \\gamma (|\\epsilon_{t-1}| - \\mathbb{E}(|\\epsilon_{t-1}|)) + \\beta \\log(\\sigma_{t-1}^2),\n",
        "\\end{align*} em que $\\epsilon_t$ é _iid_ com média zero e variância 1.\n",
        "\n",
        "A especificaão logaritmica faz com que a variância nunca seja negativa, o que, consequentemente, faz com que não exista restricão para os parâmetros. Note que se $\\alpha = 0$, choques positivos tem o mesmo efeito do que choques negativos na volatilidade. Se $\\alpha \\neq 0$ o efeito de choques positivos e negativos na volatilidade é diferente (assimétrico). Se $\\alpha < 0$, choques negativos aumentam a volatilidade mais do que choques positivos."
      ],
      "metadata": {
        "id": "hSrUobMOP6zM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "spec <- ugarchspec(mean.model = list(armaOrder = c(0, 0), include.mean = FALSE),\n",
        "                   variance.model = list(model = 'eGARCH', garchOrder = c(1, 1)),\n",
        "                   distribution = 'norm')\n",
        "fit_03 <- ugarchfit(spec, serie_c, solver = 'hybrid')\n",
        "fit_03"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "jN7P3Cq5RFvr",
        "outputId": "70eff89a-ae28-4d4e-b7f8-1e54505ed719"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "*---------------------------------*\n",
              "*          GARCH Model Fit        *\n",
              "*---------------------------------*\n",
              "\n",
              "Conditional Variance Dynamics \t\n",
              "-----------------------------------\n",
              "GARCH Model\t: eGARCH(1,1)\n",
              "Mean Model\t: ARFIMA(0,0,0)\n",
              "Distribution\t: norm \n",
              "\n",
              "Optimal Parameters\n",
              "------------------------------------\n",
              "        Estimate  Std. Error  t value Pr(>|t|)\n",
              "omega  -0.390886    0.261918  -1.4924 0.135595\n",
              "alpha1  0.028233    0.027463   1.0281 0.303921\n",
              "beta1   0.853357    0.097924   8.7145 0.000000\n",
              "gamma1  0.123392    0.049680   2.4837 0.013002\n",
              "\n",
              "Robust Standard Errors:\n",
              "        Estimate  Std. Error  t value Pr(>|t|)\n",
              "omega  -0.390886    0.238855  -1.6365 0.101735\n",
              "alpha1  0.028233    0.026492   1.0657 0.286552\n",
              "beta1   0.853357    0.089877   9.4947 0.000000\n",
              "gamma1  0.123392    0.045835   2.6921 0.007101\n",
              "\n",
              "LogLikelihood : -81.52144 \n",
              "\n",
              "Information Criteria\n",
              "------------------------------------\n",
              "                    \n",
              "Akaike       0.17104\n",
              "Bayes        0.19067\n",
              "Shibata      0.17101\n",
              "Hannan-Quinn 0.17850\n",
              "\n",
              "Weighted Ljung-Box Test on Standardized Residuals\n",
              "------------------------------------\n",
              "                        statistic p-value\n",
              "Lag[1]                      1.277  0.2585\n",
              "Lag[2*(p+q)+(p+q)-1][2]     1.534  0.3533\n",
              "Lag[4*(p+q)+(p+q)-1][5]     2.320  0.5451\n",
              "d.o.f=0\n",
              "H0 : No serial correlation\n",
              "\n",
              "Weighted Ljung-Box Test on Standardized Squared Residuals\n",
              "------------------------------------\n",
              "                        statistic p-value\n",
              "Lag[1]                      1.389  0.2386\n",
              "Lag[2*(p+q)+(p+q)-1][5]     3.633  0.3035\n",
              "Lag[4*(p+q)+(p+q)-1][9]     5.132  0.4103\n",
              "d.o.f=2\n",
              "\n",
              "Weighted ARCH LM Tests\n",
              "------------------------------------\n",
              "            Statistic Shape Scale P-Value\n",
              "ARCH Lag[3]     2.065 0.500 2.000  0.1508\n",
              "ARCH Lag[5]     3.129 1.440 1.667  0.2716\n",
              "ARCH Lag[7]     3.878 2.315 1.543  0.3645\n",
              "\n",
              "Nyblom stability test\n",
              "------------------------------------\n",
              "Joint Statistic:  0.4983\n",
              "Individual Statistics:              \n",
              "omega  0.27887\n",
              "alpha1 0.11910\n",
              "beta1  0.27952\n",
              "gamma1 0.04563\n",
              "\n",
              "Asymptotic Critical Values (10% 5% 1%)\n",
              "Joint Statistic:     \t 1.07 1.24 1.6\n",
              "Individual Statistic:\t 0.35 0.47 0.75\n",
              "\n",
              "Sign Bias Test\n",
              "------------------------------------\n",
              "                   t-value   prob sig\n",
              "Sign Bias           0.4944 0.6211    \n",
              "Negative Sign Bias  0.1496 0.8811    \n",
              "Positive Sign Bias  0.5597 0.5758    \n",
              "Joint Effect        0.5403 0.9100    \n",
              "\n",
              "\n",
              "Adjusted Pearson Goodness-of-Fit Test:\n",
              "------------------------------------\n",
              "  group statistic p-value(g-1)\n",
              "1    20     11.40       0.9096\n",
              "2    30     19.94       0.8948\n",
              "3    40     30.48       0.8336\n",
              "4    50     48.00       0.5136\n",
              "\n",
              "\n",
              "Elapsed time : 0.1725087 \n"
            ]
          },
          "metadata": {}
        }
      ]
    }
  ]
}