07_ARMA_and_ARIMA.ipynb

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      "name": "07-ARMA-and-ARIMA.ipynb",
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Am3Oj64sZ7Np",
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      "source": [
        "# ARMA(p,q) and ARIMA(p,d,q)\n",
        "# Autoregressive Moving Averages\n",
        " <em>Autoregressive Moving Averages</em> (ARMA) and <em>Autoregressive Integrated Moving Averages</em> (ARIMA).\n",
        "\n",
        "Recall that an <strong>AR(1)</strong> model follows the formula\n",
        "\n",
        "&nbsp;&nbsp;&nbsp;&nbsp;$y_{t} = c + \\phi_{1}y_{t-1} + \\varepsilon_{t}$\n",
        "\n",
        "while an <strong>MA(1)</strong> model follows the formula\n",
        "\n",
        "&nbsp;&nbsp;&nbsp;&nbsp;$y_{t} = \\mu + \\theta_{1}\\varepsilon_{t-1} + \\varepsilon_{t}$\n",
        "\n",
        "where $c$ is a constant, $\\mu$ is the expectation of $y_{t}$ (often assumed to be zero), $\\phi_1$ (phi-sub-one) is the AR lag coefficient, $\\theta_1$ (theta-sub-one) is the MA lag coefficient, and $\\varepsilon$ (epsilon) is white noise.\n",
        "\n",
        "An <strong>ARMA(1,1)</strong> model therefore follows\n",
        "\n",
        "&nbsp;&nbsp;&nbsp;&nbsp;$y_{t} = c + \\phi_{1}y_{t-1} + \\theta_{1}\\varepsilon_{t-1} + \\varepsilon_{t}$\n",
        "\n",
        "ARMA models can be used on stationary datasets.\n",
        "\n",
        "For non-stationary datasets with a trend component, ARIMA models apply a differencing coefficient as well.\n"
      ]
    },
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      "cell_type": "markdown",
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      "source": [
        "## Imports"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e2X228z7Z7Ns",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "%matplotlib inline\n",
        "\n",
        "# Load specific forecasting tools\n",
        "from statsmodels.tsa.arima_model import ARMA,ARMAResults,ARIMA,ARIMAResults\n",
        "from statsmodels.graphics.tsaplots import plot_acf,plot_pacf # for determining (p,q) orders\n",
        "from pmdarima import auto_arima # for determining ARIMA orders\n",
        "\n",
        "# Ignore harmless warnings\n",
        "import warnings\n",
        "warnings.filterwarnings(\"ignore\")\n",
        "\n",
        "# Load datasets\n",
        "df1 = pd.read_csv('../Data/DailyTotalFemaleBirths.csv',index_col='Date',parse_dates=True)\n",
        "df1.index.freq = 'D'\n",
        "df1 = df1[:120]  # we only want the first four months\n",
        "\n",
        "df2 = pd.read_csv('../Data/TradeInventories.csv',index_col='Date',parse_dates=True)\n",
        "df2.index.freq='MS'"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sd9RmNNjZ7Ny",
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      "source": [
        "## Augmented Dickey-Fuller Test to check whether it's stationary or not.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zMEwD218Z7Nz",
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      "source": [
        "from statsmodels.tsa.stattools import adfuller\n",
        "\n",
        "def adf_test(series,title=''):\n",
        "    \"\"\"\n",
        "    Pass in a time series and an optional title, returns an ADF report\n",
        "    \"\"\"\n",
        "    print(f'Augmented Dickey-Fuller Test: {title}')\n",
        "    result = adfuller(series.dropna(),autolag='AIC') # .dropna() handles differenced data\n",
        "    \n",
        "    labels = ['ADF test statistic','p-value','# lags used','# observations']\n",
        "    out = pd.Series(result[0:4],index=labels)\n",
        "\n",
        "    for key,val in result[4].items():\n",
        "        out[f'critical value ({key})']=val\n",
        "        \n",
        "    print(out.to_string())          # .to_string() removes the line \"dtype: float64\"\n",
        "    \n",
        "    if result[1] <= 0.05:\n",
        "        print(\"Strong evidence against the null hypothesis\")\n",
        "        print(\"Reject the null hypothesis\")\n",
        "        print(\"Data has no unit root and is stationary\")\n",
        "    else:\n",
        "        print(\"Weak evidence against the null hypothesis\")\n",
        "        print(\"Fail to reject the null hypothesis\")\n",
        "        print(\"Data has a unit root and is non-stationary\")"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f3F7jlg6Z7N4",
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      },
      "source": [
        "___\n",
        "## Autoregressive Moving Average - ARMA(p,q)\n",
        "we'll look at a stationary dataset, determine (p,q) orders, and run a forecasting ARMA model fit to the data\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fZLYKasLZ7N6",
        "colab_type": "code",
        "outputId": "254581eb-61dd-47d4-b4b6-3579d9aea01d",
        "colab": {}
      },
      "source": [
        "df1['Births'].plot(figsize=(12,5));"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 864x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ejuQCToyZ7OB",
        "colab_type": "text"
      },
      "source": [
        "### Run the augmented Dickey-Fuller Test to confirm stationarity"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NBFlFEBrZ7OC",
        "colab_type": "code",
        "outputId": "820be408-4edc-4db8-d64a-3fcafc32587c",
        "colab": {}
      },
      "source": [
        "adf_test(df1['Births'])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Augmented Dickey-Fuller Test: None\n",
            "ADF test statistic     -9.855384e+00\n",
            "p-value                 4.373545e-17\n",
            "# lags used             0.000000e+00\n",
            "# observations          1.190000e+02\n",
            "critical value (1%)    -3.486535e+00\n",
            "critical value (5%)    -2.886151e+00\n",
            "critical value (10%)   -2.579896e+00\n",
            "Strong evidence against the null hypothesis\n",
            "Reject the null hypothesis\n",
            "Data has no unit root and is stationary\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FzLNRwCKZ7OF",
        "colab_type": "text"
      },
      "source": [
        "### Determine the (p,q) ARMA Orders\n",
        "It should give just $p$ and $q$ value recommendations for this dataset."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "obUFGXl8Z7OG",
        "colab_type": "code",
        "outputId": "d28671a3-1e54-47c9-8311-84672cf94249",
        "colab": {}
      },
      "source": [
        "auto_arima(df1['Births'],seasonal=False).summary()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>         <td>y</td>        <th>  No. Observations:  </th>    <td>120</td>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(2, 2)</td>    <th>  Log Likelihood     </th> <td>-405.370</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>6.991</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Sat, 23 Mar 2019</td> <th>  AIC                </th>  <td>822.741</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>12:02:45</td>     <th>  BIC                </th>  <td>839.466</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>                <td>0</td>        <th>  HQIC               </th>  <td>829.533</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                       <td> </td>        <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "     <td></td>        <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>   <td>   39.8162</td> <td>    0.108</td> <td>  368.841</td> <td> 0.000</td> <td>   39.605</td> <td>   40.028</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.y</th> <td>    1.8568</td> <td>    0.081</td> <td>   22.933</td> <td> 0.000</td> <td>    1.698</td> <td>    2.016</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2.y</th> <td>   -0.8814</td> <td>    0.073</td> <td>  -12.030</td> <td> 0.000</td> <td>   -1.025</td> <td>   -0.738</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.y</th> <td>   -1.8634</td> <td>    0.109</td> <td>  -17.126</td> <td> 0.000</td> <td>   -2.077</td> <td>   -1.650</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L2.y</th> <td>    0.8634</td> <td>    0.108</td> <td>    8.020</td> <td> 0.000</td> <td>    0.652</td> <td>    1.074</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           1.0533</td> <td>          -0.1582j</td> <td>           1.0652</td> <td>          -0.0237</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.2</th> <td>           1.0533</td> <td>          +0.1582j</td> <td>           1.0652</td> <td>           0.0237</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           1.0000</td> <td>          +0.0000j</td> <td>           1.0000</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.2</th> <td>           1.1583</td> <td>          +0.0000j</td> <td>           1.1583</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                      y   No. Observations:                  120\n",
              "Model:                     ARMA(2, 2)   Log Likelihood                -405.370\n",
              "Method:                       css-mle   S.D. of innovations              6.991\n",
              "Date:                Sat, 23 Mar 2019   AIC                            822.741\n",
              "Time:                        12:02:45   BIC                            839.466\n",
              "Sample:                             0   HQIC                           829.533\n",
              "                                                                              \n",
              "==============================================================================\n",
              "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const         39.8162      0.108    368.841      0.000      39.605      40.028\n",
              "ar.L1.y        1.8568      0.081     22.933      0.000       1.698       2.016\n",
              "ar.L2.y       -0.8814      0.073    -12.030      0.000      -1.025      -0.738\n",
              "ma.L1.y       -1.8634      0.109    -17.126      0.000      -2.077      -1.650\n",
              "ma.L2.y        0.8634      0.108      8.020      0.000       0.652       1.074\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            1.0533           -0.1582j            1.0652           -0.0237\n",
              "AR.2            1.0533           +0.1582j            1.0652            0.0237\n",
              "MA.1            1.0000           +0.0000j            1.0000            0.0000\n",
              "MA.2            1.1583           +0.0000j            1.1583            0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2dGVTuY6Z7OJ",
        "colab_type": "text"
      },
      "source": [
        "### Split the data into train/test sets\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AB7B_ij2Z7OJ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Set one month for testing\n",
        "train = df1.iloc[:90]\n",
        "test = df1.iloc[90:]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RB1gIUsJZ7ON",
        "colab_type": "text"
      },
      "source": [
        "## ARMA(p,q) Model\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IX2bI4utZ7OO",
        "colab_type": "code",
        "outputId": "9096c85b-86e2-4d91-c630-bcbf7c783f1c",
        "colab": {}
      },
      "source": [
        "model = ARMA(train['Births'],order=(2,2))\n",
        "results = model.fit()\n",
        "results.summary()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>      <td>Births</td>      <th>  No. Observations:  </th>    <td>90</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>            <td>ARMA(2, 2)</td>    <th>  Log Likelihood     </th> <td>-307.905</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th>   <td>7.405</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Sat, 23 Mar 2019</td> <th>  AIC                </th>  <td>627.809</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>12:08:30</td>     <th>  BIC                </th>  <td>642.808</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>01-01-1959</td>    <th>  HQIC               </th>  <td>633.858</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 03-31-1959</td>   <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "        <td></td>          <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>        <td>   39.7549</td> <td>    0.912</td> <td>   43.607</td> <td> 0.000</td> <td>   37.968</td> <td>   41.542</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.Births</th> <td>   -0.1850</td> <td>    1.087</td> <td>   -0.170</td> <td> 0.865</td> <td>   -2.315</td> <td>    1.945</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L2.Births</th> <td>    0.4352</td> <td>    0.644</td> <td>    0.675</td> <td> 0.501</td> <td>   -0.828</td> <td>    1.698</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.Births</th> <td>    0.2777</td> <td>    1.097</td> <td>    0.253</td> <td> 0.801</td> <td>   -1.872</td> <td>    2.427</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L2.Births</th> <td>   -0.3999</td> <td>    0.679</td> <td>   -0.589</td> <td> 0.557</td> <td>   -1.730</td> <td>    0.930</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>          -1.3181</td> <td>          +0.0000j</td> <td>           1.3181</td> <td>           0.5000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.2</th> <td>           1.7434</td> <td>          +0.0000j</td> <td>           1.7434</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>          -1.2718</td> <td>          +0.0000j</td> <td>           1.2718</td> <td>           0.5000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.2</th> <td>           1.9662</td> <td>          +0.0000j</td> <td>           1.9662</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                              ARMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                 Births   No. Observations:                   90\n",
              "Model:                     ARMA(2, 2)   Log Likelihood                -307.905\n",
              "Method:                       css-mle   S.D. of innovations              7.405\n",
              "Date:                Sat, 23 Mar 2019   AIC                            627.809\n",
              "Time:                        12:08:30   BIC                            642.808\n",
              "Sample:                    01-01-1959   HQIC                           633.858\n",
              "                         - 03-31-1959                                         \n",
              "================================================================================\n",
              "                   coef    std err          z      P>|z|      [0.025      0.975]\n",
              "--------------------------------------------------------------------------------\n",
              "const           39.7549      0.912     43.607      0.000      37.968      41.542\n",
              "ar.L1.Births    -0.1850      1.087     -0.170      0.865      -2.315       1.945\n",
              "ar.L2.Births     0.4352      0.644      0.675      0.501      -0.828       1.698\n",
              "ma.L1.Births     0.2777      1.097      0.253      0.801      -1.872       2.427\n",
              "ma.L2.Births    -0.3999      0.679     -0.589      0.557      -1.730       0.930\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1           -1.3181           +0.0000j            1.3181            0.5000\n",
              "AR.2            1.7434           +0.0000j            1.7434            0.0000\n",
              "MA.1           -1.2718           +0.0000j            1.2718            0.5000\n",
              "MA.2            1.9662           +0.0000j            1.9662            0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0aWOHQkGZ7OS",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#Make predictions\n",
        "start=len(train)\n",
        "end=len(train)+len(test)-1\n",
        "predictions = results.predict(start=start, end=end).rename('ARMA(2,2) Predictions')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Gm-gAFHOZ7OW",
        "colab_type": "text"
      },
      "source": [
        "### Plot predictions against known values"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vsCHvGzwZ7OW",
        "colab_type": "code",
        "outputId": "f6451266-a920-48a7-9f06-fe5afb537ce3",
        "colab": {}
      },
      "source": [
        "title = 'Daily Total Female Births'\n",
        "ylabel='Births'\n",
        "xlabel='' # we don't really need a label here\n",
        "\n",
        "ax = test['Births'].plot(legend=True,figsize=(12,6),title=title)\n",
        "predictions.plot(legend=True)\n",
        "ax.autoscale(axis='x',tight=True)\n",
        "ax.set(xlabel=xlabel, ylabel=ylabel);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z01ElfEjZ7Ob",
        "colab_type": "text"
      },
      "source": [
        "Since our starting dataset exhibited no trend or seasonal component, this prediction makes sense."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8dEpSbeDZ7Ob",
        "colab_type": "text"
      },
      "source": [
        "___\n",
        "## Autoregressive Integrated Moving Average - ARIMA(p,d,q)\n",
        "The steps are the same as for ARMA(p,q), except that we'll apply a differencing component to make the dataset stationary.<br>\n",
        "First let's take a look at the <em>Real Manufacturing and Trade Inventories</em> dataset.\n",
        "### Plot the Source Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "4biR0ufDZ7Oc",
        "colab_type": "code",
        "outputId": "3f7f099f-6344-4d1b-d13d-eae7d3ec4402",
        "colab": {}
      },
      "source": [
        "# HERE'S A TRICK TO ADD COMMAS TO Y-AXIS TICK VALUES\n",
        "import matplotlib.ticker as ticker\n",
        "formatter = ticker.StrMethodFormatter('{x:,.0f}')\n",
        "\n",
        "title = 'Real Manufacturing and Trade Inventories'\n",
        "ylabel='Chained 2012 Dollars'\n",
        "xlabel='' # we don't really need a label here\n",
        "\n",
        "ax = df2['Inventories'].plot(figsize=(12,5),title=title)\n",
        "ax.autoscale(axis='x',tight=True)\n",
        "ax.set(xlabel=xlabel, ylabel=ylabel)\n",
        "ax.yaxis.set_major_formatter(formatter);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ia0Yig-0Z7Oe",
        "colab_type": "text"
      },
      "source": [
        "### Run an ETS Decomposition \n",
        "We probably won't learn a lot from it."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "4DH9ETjGZ7Of",
        "colab_type": "code",
        "outputId": "bc5e878e-02c8-450a-81a0-8127952657d5",
        "colab": {}
      },
      "source": [
        "from statsmodels.tsa.seasonal import seasonal_decompose\n",
        "\n",
        "result = seasonal_decompose(df2['Inventories'], model='additive')  # model='add' also works\n",
        "result.plot();"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OsGuUeFBZ7Oi",
        "colab_type": "text"
      },
      "source": [
        "Here we see that the seasonal component does not contribute significantly to the behavior of the series.\n",
        "### Determine ARIMA Orders"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "z5DBjjLkZ7Oj",
        "colab_type": "code",
        "outputId": "c6eb2993-f26a-48ca-c2ba-f44239faf2b5",
        "colab": {}
      },
      "source": [
        "auto_arima(df2['Inventories'],seasonal=False).summary()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARIMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>        <td>D.y</td>       <th>  No. Observations:  </th>    <td>263</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>          <td>ARIMA(1, 1, 1)</td>  <th>  Log Likelihood     </th> <td>-2610.252</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th> <td>4938.258</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Sat, 23 Mar 2019</td> <th>  AIC                </th> <td>5228.505</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>12:18:53</td>     <th>  BIC                </th> <td>5242.794</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>                <td>1</td>        <th>  HQIC               </th> <td>5234.247</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                       <td> </td>        <th>                     </th>     <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "      <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>     <td> 3472.9857</td> <td> 1313.669</td> <td>    2.644</td> <td> 0.009</td> <td>  898.241</td> <td> 6047.731</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.D.y</th> <td>    0.9037</td> <td>    0.039</td> <td>   23.414</td> <td> 0.000</td> <td>    0.828</td> <td>    0.979</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.D.y</th> <td>   -0.5732</td> <td>    0.076</td> <td>   -7.545</td> <td> 0.000</td> <td>   -0.722</td> <td>   -0.424</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           1.1065</td> <td>          +0.0000j</td> <td>           1.1065</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           1.7446</td> <td>          +0.0000j</td> <td>           1.7446</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                             ARIMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                    D.y   No. Observations:                  263\n",
              "Model:                 ARIMA(1, 1, 1)   Log Likelihood               -2610.252\n",
              "Method:                       css-mle   S.D. of innovations           4938.258\n",
              "Date:                Sat, 23 Mar 2019   AIC                           5228.505\n",
              "Time:                        12:18:53   BIC                           5242.794\n",
              "Sample:                             1   HQIC                          5234.247\n",
              "                                                                              \n",
              "==============================================================================\n",
              "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const       3472.9857   1313.669      2.644      0.009     898.241    6047.731\n",
              "ar.L1.D.y      0.9037      0.039     23.414      0.000       0.828       0.979\n",
              "ma.L1.D.y     -0.5732      0.076     -7.545      0.000      -0.722      -0.424\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            1.1065           +0.0000j            1.1065            0.0000\n",
              "MA.1            1.7446           +0.0000j            1.7446            0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ARy3-QcHZ7On",
        "colab_type": "text"
      },
      "source": [
        "This suggests that we should fit an ARIMA(1,1,1) model to best forecast future values of the series. Before we train the model, let's look at augmented Dickey-Fuller Test, and the ACF/PACF plots to see if they agree."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IU3vsZouZ7On",
        "colab_type": "text"
      },
      "source": [
        "### Run the augmented Dickey-Fuller Test on the First Difference"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "Gxp1m5WzZ7Oo",
        "colab_type": "code",
        "outputId": "bcbe5b9f-fb1f-4fba-fb2e-29789c1ffd2e",
        "colab": {}
      },
      "source": [
        "from statsmodels.tsa.statespace.tools import diff\n",
        "df2['d1'] = diff(df2['Inventories'],k_diff=1)\n",
        "\n",
        "# Equivalent to:\n",
        "# df1['d1'] = df1['Inventories'] - df1['Inventories'].shift(1)\n",
        "\n",
        "adf_test(df2['d1'],'Real Manufacturing and Trade Inventories')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Augmented Dickey-Fuller Test: Real Manufacturing and Trade Inventories\n",
            "ADF test statistic       -3.412249\n",
            "p-value                   0.010548\n",
            "# lags used               4.000000\n",
            "# observations          258.000000\n",
            "critical value (1%)      -3.455953\n",
            "critical value (5%)      -2.872809\n",
            "critical value (10%)     -2.572775\n",
            "Strong evidence against the null hypothesis\n",
            "Reject the null hypothesis\n",
            "Data has no unit root and is stationary\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BZSvZm3FZ7Or",
        "colab_type": "text"
      },
      "source": [
        "This confirms that we reached stationarity after the first difference.\n",
        "### Run the ACF and PACF plots\n",
        "A <strong>PACF Plot</strong> can reveal recommended AR(p) orders, and an <strong>ACF Plot</strong> can do the same for MA(q) orders.<br>\n",
        "Alternatively, we can compare the stepwise <a href='https://en.wikipedia.org/wiki/Akaike_information_criterion'>Akaike Information Criterion (AIC)</a> values across a set of different (p,q) combinations to choose the best combination."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O4pm3qfpZ7Os",
        "colab_type": "code",
        "outputId": "16d607f3-2368-41b8-a594-834cb65bf8ae",
        "colab": {}
      },
      "source": [
        "title = 'Autocorrelation: Real Manufacturing and Trade Inventories'\n",
        "lags = 40\n",
        "plot_acf(df2['Inventories'],title=title,lags=lags);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wCtACgiLZ7Ow",
        "colab_type": "code",
        "outputId": "8b9b3a95-96f7-44d5-88b4-a99639842864",
        "colab": {}
      },
      "source": [
        "title = 'Partial Autocorrelation: Real Manufacturing and Trade Inventories'\n",
        "lags = 40\n",
        "plot_pacf(df2['Inventories'],title=title,lags=lags);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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WAR25s4mI75H+ymI9p5D+TG1ExG3AJEmt/sW7lt167wZWrt3MM9v7COCZ7X2sXLuZW+/dAPiux8ysW4bqhzpn0P9vd6zL0x6uXlDSueQ/rjV79uzq2Q3dtf5Jtm7v//d7tm7v4+71T7LoiGm+6zEz65KhekGgVm9e87YiIi6LiIURsXDq1IH9xoUXTj+ACeN6+02bMK6X+dMPaHrXY2Zm5RmqZLOO/n/reybpr+d11KIjprFg1iTUtx1iF/vmu5dFR0xreNdjZmblGqpksxQ4M7+Vdizw64jYYwitXb094qpzjmHqfd9k0rof8H+XvHT3MFmjux4zMytXR57ZSLoaWARMkbQO+DAwFiAiPg8sA04EVgHPAG/vRLm19PaIfTevZt/Nq3nVkYfsnl656/nRLx8mesaw7/ixu+96zMysXB1JNhGxpMn8AN7dibIGq3LX87I3nsP2/abx6Q/9OYuOmOaXA8zMhsCw/hMDnVbvrsfMzMrlX1djZmalc7IxM7PSOdmYmVnpnGzMzKx0TjZmZlY6JxszMyudk42ZmZXOycbMzErnZGNmZqVzsjEzs9I52ZiZWemcbMzMrHRONmZmVjonGzMzK52TjZmZlc7JxszMSudkY2ZmpXOyMTOz0jnZmJlZ6ZxszMysdE42ZmZWOicbMzMrnZONmZmVzsnGzMxK52RjZmal60iykbRY0r2SVkm6oMb82ZJukfRTST+XdGInyjUzs5Gh7WQjqRe4FDgBmA8skTS/arEPAddFxEuB04F/brdcMzMbOTpxZ3M0sCoiVkfEduAa4JSqZQI4IH8+EFjfgXLNzGyEGNOBbcwA1ha+rwOOqVrmIuA7kv4M2A84vgPlmpnZCNGJOxvVmBZV35cAV0bETOBE4CpJNcuWdK6kFZJWbNy4sQPhmZlZt3Ui2awDZhW+z2TPYbJzgOsAIuJHwD7AlFobi4jLImJhRCycOnVqB8IzM7Nu60SyWQ7Mk3SopHGkFwCWVi3zIPAqAElHkpKNb1vMzPYSbSebiNgJnAfcCNxDeuvsLkkXSzo5L/Y+4I8l/Qy4Gjg7IqqH2szMbJTqxAsCRMQyYFnVtAsLn+8GjutEWWZmNvL4NwiYmVnpnGzMzKx0TjZmZlY6JxszMyudk42ZmZXOycbMzErnZGNmZqVzsjEzs9I52ZiZWemcbMzMrHRONmZmVjonGzMzK52TjZmZlc7JxszMSudkY2ZmpXOyMTOz0jnZmJlZ6ZxszMysdE42ZmZWOicbMzMrnZONmZmVzsnGzMxK52RjZmalc7IxM7PSOdmYmVnpnGzMzKx0TjZmZla6jiQbSYsl3StplaQL6izzh5LulnSXpK90olwzMxsZxrS7AUm9wKXAq4F1wHJJSyPi7sIy84D3A8dFxBOSprVbrpmZjRyduLM5GlgVEasjYjtwDXBK1TJ/DFwaEU8ARMSGDpRrZmYjRCeSzQxgbeH7ujyt6PnA8yX9QNJtkhbX25ikcyWtkLRi48aNHQjPzMy6rRPJRjWmRdX3McA8YBGwBLhc0qRaG4uIyyJiYUQsnDp1agfCMzOzbutEslkHzCp8nwmsr7HMf0TEjoj4FXAvKfmYmdleoBPJZjkwT9KhksYBpwNLq5b5BvAKAElTSMNqqztQtpmZjQBtJ5uI2AmcB9wI3ANcFxF3SbpY0sl5sRuBTZLuBm4B/jIiNrVbtpmZjQxtv/oMEBHLgGVV0y4sfA7gL/I/MzPby/g3CJiZWemcbMzMrHRONmZmVjonGzMzK52TjZmZlc7JxszMSudkY2ZmpXOyMTOz0jnZmJlZ6ZxszMysdE42ZmZWOicbMzMrnZONmZmVzsnGzMxK52RjZmalc7IxM7PSOdmYmVnpnGzMzKx0TjZmZlY6JxszMyudk42ZmZXOycbMzErnZGNmZqVzsjEzs9I52ZiZWemcbMzMrHQdSTaSFku6V9IqSRc0WO5USSFpYSfKNTOzkaHtZCOpF7gUOAGYDyyRNL/GcvsD7wF+3G6ZZmY2snTizuZoYFVErI6I7cA1wCk1lvsocAnwbAfKNDOzEaQTyWYGsLbwfV2etpuklwKzIuJbzTYm6VxJKySt2LhxYwfCMzOzbutEslGNabF7ptQDfAZ4Xysbi4jLImJhRCycOnVqB8IzM7Nu60SyWQfMKnyfCawvfN8feBFwq6Q1wLHAUr8kYGa29+hEslkOzJN0qKRxwOnA0srMiPh1REyJiLkRMRe4DTg5IlZ0oGwzMxsB2k42EbETOA+4EbgHuC4i7pJ0saST292+mZmNfGM6sZGIWAYsq5p2YZ1lF3WiTDMzGzn8GwTMzKx0TjZmZlY6JxszMyudk42ZmZXOycbMzErnZGNmZqVzsjEzs9I52ZiZWemcbMzMrHRONmZmVjonGzMzK52TjZmZlc7JxszMSudkY2ZmpXOyMTOz0jnZmJlZ6ZxszMysdE42ZmZWOicbMzMrnZONmZmVzsnGzMxK52RjZmalc7IxM7PSOdmYmVnpnGzMzKx0TjZmZla6jiQbSYsl3StplaQLasz/C0l3S/q5pJskzelEuWZmNjK0nWwk9QKXAicA84ElkuZXLfZTYGFEvBi4Hrik3XLNzGzk6MSdzdHAqohYHRHbgWuAU4oLRMQtEfFM/nobMLMD5ZqZ2QjRiWQzA1hb+L4uT6vnHOCGejMlnStphaQVGzdu7EB4ZmbWbZ1INqoxLWouKL0VWAh8qt7GIuKyiFgYEQunTp3agfDMzKzbxnRgG+uAWYXvM4H11QtJOh74IPD7EbGtA+WamdkI0Yk7m+XAPEmHShoHnA4sLS4g6aXAvwAnR8SGDpRpZmYjSNvJJiJ2AucBNwL3ANdFxF2SLpZ0cl7sU8BE4KuSVkpaWmdzZmY2CnViGI2IWAYsq5p2YeHz8Z0ox8zMRib/BgEzMyudk42ZmZXOycbMzErnZGNmZqVzsjEzs9I52ZiZWemcbMzMrHRONmZmVrqO/FDnSPPk1h386P5N3Q7DzKymlx02udshdJzvbMzMrHRONmZmVjonGzMzK52TjZmZlc7JxszMSudkY2ZmpXOyMTOz0jnZmJlZ6ZxszMysdE42ZmZWOicbMzMrnZONmZmVzsnGzMxK52RjZmalc7IxM7PS7ZV/z8bM9m67dgUr125mzaanmTt5PxbMmkRPj7od1qjmZGO2l9vbOt5du4JP3HAPqzZsYfvOXYwb08Ph0ybygROO7Pp+V47F8jWP88LpB7DoiGn0jpJj0ZFkI2kx8I9AL3B5RPxt1fzxwJeB3wI2AadFxJpOlD1c7G0nbLtcX8PDcO5429Gofa1cu5lVG7awbecuALbt3MWqDVtYuXYzR805qKsxF4/FhHG9LJg1iavOOWZUJJy2k42kXuBS4NXAOmC5pKURcXdhsXOAJyLicEmnA58ETmu37OFitJ6wzTRLGPXmt1JfZSajdrY9UpNkvbiHa8fbjmbta82mp9me97di+85drNn09O597kYbqT4Wz2zvY+Xazdx67wZedeQhA6yF4acTdzZHA6siYjWApGuAU4BisjkFuCh/vh74J0mKiOhA+R3TqUZS64QdbR1csxO60fxm9VVm8m4l7np1XXaSLOs4N4q7lY53uBpsAp07eT/GjenZPR9g3Jge5k7eb/d2B9v+2lm31rHYur2Pu9c/OSqSjdrt7yWdCiyOiHfk728DjomI8wrL3JmXWZe/35+XeazRtg+ec2S8+gNfGHBMK3+2EoAFL1lQc15fXzBv/ov6TY8IHnx8K1t39BEBEkwY28vsgycgNW4kG5/axmNbtu8xferEcUzZf3zTbUcEW7b18eyOPvYZ28vE8b27y2wnrlY0KruRp57dyUObt1JsPhLMmDSB/fcZ03D+szv6GtZXs223o9G2J47vbVjXzeJq51i1e5wbHcdGcQNt1XWz9jPY9tVs3Ub19diW7S2dj89s2wEI9WjAx3kwdV2pz3rr11q3R3D4tIkctO+4luoM4Lp3vfz2iFjY8gpDpBN3NrVaTnUGa2WZtKB0LnAuwMTnHjaogGolmeK8J5/dscf0Ldv6djdcgAjYuqOPLdv6+p109919J0C/ZLXP2F4k9mhg48f2Nt12pYOr1/DbiavZvGYnXaN1ny3E9JvtwbYdKa5G85vVV7NtV2L/5arV0DuO6dOfu0dHVG9eo20DDeu6WVytHKt69dls3Wb72+g4Nop78sRxTBjbu0enPXF8b7/la8XdrNxW2le9/Wq2bqP6ata+JDH74Als2TaObTv6GF+VMBrVV7PztVkbabRfE8f39jsWPYKJ48cwacJYRoNOJJt1wKzC95nA+jrLrJM0BjgQeLzWxiLiMuAygIULF8a173xZB0Ls70f3b9pj2tfuWMf1t6+rCgZe9rzJvPGombsnvfsr7wfgwvOX7p7W7Na50bbnTt6Pz958Hyj9yFME9O0KXvfiGRw156CW4tq1K3jnjVfQN/EQTvpfr9lj6KfevDseeKJh2fX2t7hucShi/Jgezn75oRw156CG8xfMmtSwvpptu1Lfu/aZBL1j2PjUNg6ckNYH6s5rtu01m55uWNfN4mp2rBodi0brvn7BjJb2qd5xbKU+mz17qxV3q+XWm9/oOK5cu3nQ50WlvgY7DNuovoC26rqVOlm5djO7Ipg/yLfRrnvXgBYfMp1INsuBeZIOBR4CTgfOqFpmKXAW8CPgVODm4fa8ptk4biM9Pdp9gtQ6YRttu9mYeavjy1vmvx56x/DZm+/bfWIBdee18qB0165g++TD6Zt4CHc88ES/fVowaxKHT5u4xwm9YNakpvOb1VezbVfG5BmThhaKY/JA3XlHzTmo6bYb1XWzdRsdq0bHqadHDddttL9HzTmo6XFsFndPjzhqzkE1n9E0irtZuc3mN9qvds6LZu2rmUb19Y2VD7VV1832q3IsXnbY5JZiHUnaTjYRsVPSecCNpFefvxARd0m6GFgREUuBK4CrJK0i3dGc3m65ndaskTTT6IQts4Nrp+Ntp3NsdkK3Mr9efTVbt9EJW/lca17lZK637VY65cEmyWYJo50OrtkFSTudb6O4m5XbbH6j49hs3XYSaDON6qvdum7nonak68jP2UTEMmBZ1bQLC5+fBd7cibLK0soJ2ehKf7DbbreDa6fjbadzrMTW6IRu94Svt26zE7bZyVxv2620gcEmyVauaAfbwbVyoTTYY9Eo7tcvmDHou1tofBzbPS/aVa++2q3rdi9qRzL/BoGCwQ4ntJpwyujg2ul42+kcu6nZCVvWHWo767dyRTvYDq7Mjred4ap27gTbPS/K0m5dl50kh7O2X30u08KFC2PFihUd326tFwSaqffg7z2vnDesfuq4+DAUGPSD0uG6vxXNfh5muJ3M7f7sULf2qewfWB6Ox2o4aOeZjaRh+eqzk02LKm+/FGtLwKm/NbPf22rdUEbHu7f+VoQyjdSOdaTGPZKNxmTjYbQWDecHe82eIwxmqGFvvt0vSzeGfTphpMZtw4uTTYv2xgd77mTMrFOcbFrkK30zs8FzshkAX+mbmQ2O/yy0mZmVzsnGzMxK52RjZmalc7IxM7PSOdmYmVnpnGzMzKx0TjZmZlY6JxszMyudk42ZmZVur/wNAqPxT66amQ1nvrMxM7PSOdmYmVnpnGzMzKx0TjZmZlY6JxszMyudk42ZmZXOycbMzErnZGNmZqVzsjEzs9IpIrodQ12SNgIPDHL1KcBjHQynUxzXwDiugXFcAzMa45oTEVM7GUwnDOtk0w5JKyJiYbfjqOa4BsZxDYzjGhjHNXQ8jGZmZqVzsjEzs9KN5mRzWbcDqMNxDYzjGhjHNTCOa4iM2mc2ZmY2fIzmOxszMxsmnGzMzKx0oy7ZSFos6V5JqyRd0O14KiStkfQ/klZKWtHlWL4gaYOkOwvTDpb0XUn35f8PGiZxXSTpoVxvKyWdOMQxzZJ0i6R7JN0l6b15elfrq0FcXa2vHMM+kn4i6Wc5to/k6YdK+nGus2sljRsmcV0p6VeFOlswlHHlGHol/VTSt/L3rtZVGUZVspHUC1wKnADMB5ZImt/dqPp5RUQsGAbvz18JLK6adgFwU0TMA27K34falewZF8Bncr0tiIhlQxzTTuCj+0++AAADP0lEQVR9EXEkcCzw7tymul1f9eKC7tYXwDbglRHxEmABsFjSscAnc2zzgCeAc4ZJXAB/WaizlUMcF8B7gXsK37tdVx03qpINcDSwKiJWR8R24BrglC7HNOxExPeAx6smnwJ8KX/+EvD6IQ2KunF1VUQ8HBF35M9PkTqEGXS5vhrE1XWRbMlfx+Z/AbwSuD5P70ad1YurqyTNBF4LXJ6/iy7XVRlGW7KZAawtfF/HMDkBSY36O5Jul3Rut4Op4ZCIeBhSRwZM63I8RedJ+nkeZhvy4b0KSXOBlwI/ZhjVV1VcMAzqKw8LrQQ2AN8F7gc2R8TOvEhXzs3quCKiUmcfz3X2GUnjhzisfwDOB3bl75MZBnXVaaMt2ajGtK5fuWTHRcRRpCG+d0v6vW4HNEJ8DjiMNOzxMPDpbgQhaSLw78D/jognuxFDLTXiGhb1FRF9EbEAmEkacTiy1mJDG9WecUl6EfB+4AXAbwMHA381VPFIOgnYEBG3FyfXWHS49GODNtqSzTpgVuH7TGB9l2LpJyLW5/83AF8nnYDDyaOSnguQ/9/Q5XgAiIhHcwexC/h/dKHeJI0ldej/FhFfy5O7Xl+14hoO9VUUEZuBW0nPlSZJGpNndfXcLMS1OA9JRkRsA77I0NbZccDJktaQhv1fSbrTGTZ11SmjLdksB+blNznGAacDS7scE5L2k7R/5TPwGuDOxmsNuaXAWfnzWcB/dDGW3SodevYGhrje8vj5FcA9EfH3hVldra96cXW7vnIMUyVNyp8nAMeTnindApyaF+tGndWK6xeFiwaRno0MWZ1FxPsjYmZEzCX1VzdHxFvocl2VYdT9BoH8quc/AL3AFyLi410OCUnPI93NAIwBvtLNuCRdDSwi/RrzR4EPA98ArgNmAw8Cb46IIX1YXyeuRaQhoQDWAO+sPCsZoph+B/hv4H/4zZj6B0jPR7pWXw3iWkIX6yvH9mLSQ+1e0gXtdRFxcT4PriENVf0UeGu+m+h2XDcDU0nDVyuBdxVeJBgykhYB/yciTup2XZVh1CUbMzMbfkbbMJqZmQ1DTjZmZlY6JxszMyudk42ZmZXOycbMzErnZGNmZqVzsjEzs9L9fx5Jkgzhx71YAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aN_CcNZvZ7O2",
        "colab_type": "text"
      },
      "source": [
        "This tells us that the AR component should be more important than MA. From the <a href='https://people.duke.edu/~rnau/411arim3.htm'>Duke University Statistical Forecasting site</a>:<br>\n",
        "> <em>If the PACF displays a sharp cutoff while the ACF decays more slowly (i.e., has significant spikes at higher lags), we    say that the stationarized series displays an \"AR signature,\" meaning that the autocorrelation pattern can be explained more    easily by adding AR terms than by adding MA terms.</em><br>\n",
        "\n",
        "Let's take a look at <tt>pmdarima.auto_arima</tt> done stepwise to see if having $p$ and $q$ terms the same still makes sense:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q3JZLofdZ7O3",
        "colab_type": "code",
        "outputId": "cd786f2f-c10a-463e-e178-50bfb8a60751",
        "colab": {}
      },
      "source": [
        "stepwise_fit = auto_arima(df2['Inventories'], start_p=0, start_q=0,\n",
        "                          max_p=2, max_q=2, m=12,\n",
        "                          seasonal=False,\n",
        "                          d=None, trace=True,\n",
        "                          error_action='ignore',   # we don't want to know if an order does not work\n",
        "                          suppress_warnings=True,  # we don't want convergence warnings\n",
        "                          stepwise=True)           # set to stepwise\n",
        "\n",
        "stepwise_fit.summary()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Fit ARIMA: order=(0, 1, 0); AIC=5348.037, BIC=5355.181, Fit time=0.004 seconds\n",
            "Fit ARIMA: order=(1, 1, 0); AIC=5250.883, BIC=5261.599, Fit time=0.050 seconds\n",
            "Fit ARIMA: order=(0, 1, 1); AIC=5283.095, BIC=5293.811, Fit time=0.020 seconds\n",
            "Fit ARIMA: order=(2, 1, 0); AIC=5240.553, BIC=5254.842, Fit time=0.100 seconds\n",
            "Fit ARIMA: order=(2, 1, 1); AIC=5229.528, BIC=5247.389, Fit time=0.104 seconds\n",
            "Fit ARIMA: order=(1, 1, 1); AIC=5228.505, BIC=5242.794, Fit time=0.109 seconds\n",
            "Fit ARIMA: order=(1, 1, 2); AIC=5229.289, BIC=5247.150, Fit time=0.157 seconds\n",
            "Fit ARIMA: order=(2, 1, 2); AIC=nan, BIC=nan, Fit time=nan seconds\n",
            "Total fit time: 0.563 seconds\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARIMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>        <td>D.y</td>       <th>  No. Observations:  </th>    <td>263</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>          <td>ARIMA(1, 1, 1)</td>  <th>  Log Likelihood     </th> <td>-2610.252</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th> <td>4938.258</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Sat, 23 Mar 2019</td> <th>  AIC                </th> <td>5228.505</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>12:19:52</td>     <th>  BIC                </th> <td>5242.794</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>                <td>1</td>        <th>  HQIC               </th> <td>5234.247</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                       <td> </td>        <th>                     </th>     <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "      <td></td>         <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>     <td> 3472.9857</td> <td> 1313.669</td> <td>    2.644</td> <td> 0.009</td> <td>  898.241</td> <td> 6047.731</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.D.y</th> <td>    0.9037</td> <td>    0.039</td> <td>   23.414</td> <td> 0.000</td> <td>    0.828</td> <td>    0.979</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.D.y</th> <td>   -0.5732</td> <td>    0.076</td> <td>   -7.545</td> <td> 0.000</td> <td>   -0.722</td> <td>   -0.424</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           1.1065</td> <td>          +0.0000j</td> <td>           1.1065</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           1.7446</td> <td>          +0.0000j</td> <td>           1.7446</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                             ARIMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:                    D.y   No. Observations:                  263\n",
              "Model:                 ARIMA(1, 1, 1)   Log Likelihood               -2610.252\n",
              "Method:                       css-mle   S.D. of innovations           4938.258\n",
              "Date:                Sat, 23 Mar 2019   AIC                           5228.505\n",
              "Time:                        12:19:52   BIC                           5242.794\n",
              "Sample:                             1   HQIC                          5234.247\n",
              "                                                                              \n",
              "==============================================================================\n",
              "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const       3472.9857   1313.669      2.644      0.009     898.241    6047.731\n",
              "ar.L1.D.y      0.9037      0.039     23.414      0.000       0.828       0.979\n",
              "ma.L1.D.y     -0.5732      0.076     -7.545      0.000      -0.722      -0.424\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            1.1065           +0.0000j            1.1065            0.0000\n",
              "MA.1            1.7446           +0.0000j            1.7446            0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F-KAClvbZ7O-",
        "colab_type": "text"
      },
      "source": [
        "Looks good from here! Now let's train & test the ARIMA(1,1,1) model, evaluate it, then produce a forecast of future values.\n",
        "### Split the data into train/test sets"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X5KwI7nVZ7O_",
        "colab_type": "code",
        "outputId": "e68aa90f-b417-4e4e-f5ad-5cb209b81fec",
        "colab": {}
      },
      "source": [
        "len(df2)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "264"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YCLCAKenZ7PF",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Set one year for testing\n",
        "train = df2.iloc[:252]\n",
        "test = df2.iloc[252:]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B8vliHtCZ7PM",
        "colab_type": "code",
        "outputId": "8c6dcba8-fdc1-4cc5-a024-95ffa9366998",
        "colab": {}
      },
      "source": [
        "model = ARIMA(train['Inventories'],order=(1,1,1))\n",
        "results = model.fit()\n",
        "results.summary()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>ARIMA Model Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>   <td>D.Inventories</td>  <th>  No. Observations:  </th>    <td>251</td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>          <td>ARIMA(1, 1, 1)</td>  <th>  Log Likelihood     </th> <td>-2486.395</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>css-mle</td>     <th>  S.D. of innovations</th> <td>4845.028</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>          <td>Sat, 23 Mar 2019</td> <th>  AIC                </th> <td>4980.790</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>              <td>12:20:09</td>     <th>  BIC                </th> <td>4994.892</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Sample:</th>           <td>02-01-1997</td>    <th>  HQIC               </th> <td>4986.465</td> \n",
              "</tr>\n",
              "<tr>\n",
              "  <th></th>                 <td>- 12-01-2017</td>   <th>                     </th>     <td> </td>    \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "           <td></td>              <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th>               <td> 3197.5697</td> <td> 1344.871</td> <td>    2.378</td> <td> 0.018</td> <td>  561.671</td> <td> 5833.468</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ar.L1.D.Inventories</th> <td>    0.9026</td> <td>    0.039</td> <td>   23.010</td> <td> 0.000</td> <td>    0.826</td> <td>    0.979</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>ma.L1.D.Inventories</th> <td>   -0.5581</td> <td>    0.079</td> <td>   -7.048</td> <td> 0.000</td> <td>   -0.713</td> <td>   -0.403</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<caption>Roots</caption>\n",
              "<tr>\n",
              "    <td></td>   <th>            Real</th>  <th>         Imaginary</th> <th>         Modulus</th>  <th>        Frequency</th>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>AR.1</th> <td>           1.1080</td> <td>          +0.0000j</td> <td>           1.1080</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>MA.1</th> <td>           1.7918</td> <td>          +0.0000j</td> <td>           1.7918</td> <td>           0.0000</td>\n",
              "</tr>\n",
              "</table>"
            ],
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                             ARIMA Model Results                              \n",
              "==============================================================================\n",
              "Dep. Variable:          D.Inventories   No. Observations:                  251\n",
              "Model:                 ARIMA(1, 1, 1)   Log Likelihood               -2486.395\n",
              "Method:                       css-mle   S.D. of innovations           4845.028\n",
              "Date:                Sat, 23 Mar 2019   AIC                           4980.790\n",
              "Time:                        12:20:09   BIC                           4994.892\n",
              "Sample:                    02-01-1997   HQIC                          4986.465\n",
              "                         - 12-01-2017                                         \n",
              "=======================================================================================\n",
              "                          coef    std err          z      P>|z|      [0.025      0.975]\n",
              "---------------------------------------------------------------------------------------\n",
              "const                3197.5697   1344.871      2.378      0.018     561.671    5833.468\n",
              "ar.L1.D.Inventories     0.9026      0.039     23.010      0.000       0.826       0.979\n",
              "ma.L1.D.Inventories    -0.5581      0.079     -7.048      0.000      -0.713      -0.403\n",
              "                                    Roots                                    \n",
              "=============================================================================\n",
              "                  Real          Imaginary           Modulus         Frequency\n",
              "-----------------------------------------------------------------------------\n",
              "AR.1            1.1080           +0.0000j            1.1080            0.0000\n",
              "MA.1            1.7918           +0.0000j            1.7918            0.0000\n",
              "-----------------------------------------------------------------------------\n",
              "\"\"\""
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LPUEqq8vZ7PU",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Obtain predicted values\n",
        "start=len(train)\n",
        "end=len(train)+len(test)-1\n",
        "predictions = results.predict(start=start, end=end, dynamic=False, typ='levels').rename('ARIMA(1,1,1) Predictions')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QceQYfbhZ7Pa",
        "colab_type": "text"
      },
      "source": [
        "Passing <tt>dynamic=False</tt> means that forecasts at each point are generated using the full history up to that point (all lagged values).\n",
        "\n",
        "Passing <tt>typ='levels'</tt> predicts the levels of the original endogenous variables. If we'd used the default <tt>typ='linear'</tt> we would have seen linear predictions in terms of the differenced endogenous variables.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8sC5EOQ5Z7Pa",
        "colab_type": "code",
        "outputId": "5be3d3ca-2bd8-4e2e-9bb3-6c6d933846b0",
        "colab": {}
      },
      "source": [
        "# Compare predictions to expected values\n",
        "for i in range(len(predictions)):\n",
        "    print(f\"predicted={predictions[i]:<11.10}, expected={test['Inventories'][i]}\")"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "predicted=2107148.333, expected=2110158\n",
            "predicted=2110526.201, expected=2118199\n",
            "predicted=2113886.499, expected=2112427\n",
            "predicted=2117230.941, expected=2112276\n",
            "predicted=2120561.071, expected=2111835\n",
            "predicted=2123878.284, expected=2109298\n",
            "predicted=2127183.839, expected=2119618\n",
            "predicted=2130478.871, expected=2127170\n",
            "predicted=2133764.405, expected=2134172\n",
            "predicted=2137041.369, expected=2144639\n",
            "predicted=2140310.596, expected=2143001\n",
            "predicted=2143572.84 , expected=2158115\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u5nitOhTZ7Pi",
        "colab_type": "code",
        "outputId": "da37fddf-93a5-4f4d-ee7a-34d3bc77cf74",
        "colab": {}
      },
      "source": [
        "# Plot predictions against known values\n",
        "title = 'Real Manufacturing and Trade Inventories'\n",
        "ylabel='Chained 2012 Dollars'\n",
        "xlabel='' # we don't really need a label here\n",
        "\n",
        "ax = test['Inventories'].plot(legend=True,figsize=(12,6),title=title)\n",
        "predictions.plot(legend=True)\n",
        "ax.autoscale(axis='x',tight=True)\n",
        "ax.set(xlabel=xlabel, ylabel=ylabel)\n",
        "ax.yaxis.set_major_formatter(formatter);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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SksIXX3zBjz/+yOmnn0737t05/fTTWblyJQBDhw7ljjvuYODAgQwfPpyRI0dyyy23AJCens7FF19Mr1696NWrF1OnTgXg888/JyUlhZSUFE444QS2b99elm+fiIiISKWhpL+S+/7773niiSeYP38+y5cvZ+rUqZx55pl8/fXX7Ny5E4A33niDyy+/nI0bN/LAAw/wySefMHPmTFJTU3nssbyNl2jUqBEzZ87kpptu4tFHH6V169b86le/4vbbb2fWrFn079+fW265hWuvvZY5c+Zw9dVXc+utt+adv3jxYj755BP+8Y9/HBDjb3/7W26//Xa+/fZb3n77ba6//noAHn30UZ5++mlmzZrFF198Qc2aNcvgHRMRERGpfDS9J4buff8H5q8p7vPIiqdLs6O45/zji12/d+/etGgRrJVOSUlhxYoV9OvXj0GDBvH+++9zySWXMGHCBP7+97/z+eefM3/+fE4++WQA9u3bx0knnZTX1kUXXQRAz549GTu24McuTJs2Le/YkCFD+MMf/pB37NJLLyUhIeGgcz755BPmz5+f93rbtm1s376dk08+mTvuuIOrr76aiy66KO86RERERI4UWdk5pdKOkv5Krnr16nm/JyQkkJWVBcDll1/O008/TYMGDejVqxd16tTB3TnzzDMZNWpU1LYi2ylK5K4ytWvXLrBOTk4O06ZNO2gk/8477+Tcc89l4sSJ9OnTh08++YROnToVq18RERGRyuBfk5eVSjtK+mOoJCPyZW3AgAFcd911PPfcc1x++eUA9OnTh5tvvpmlS5fSvn17du3aRVpaGh07diy0nTp16rBt2/5vM/r27cvo0aMZMmQIr732Gv369SsylrPOOounnnqKYcOGATBr1ixSUlJYtmwZ3bp1o1u3bkybNo2FCxcq6RcREZEjxpy0rTz56ZJSaUtz+o9QCQkJnHfeeUyaNInzzjsPgMaNGzNy5EiuvPJKunfvTp8+fVi4cGHUds4//3zeeeedvIW8I0aM4KWXXqJ79+688sorPPnkk0XGMmLECGbMmEH37t3p0qULzzzzDABPPPEEXbt2JTk5mZo1a3L22Wcf/oWLiIiIVAB7MrO5/Y1ZNE6qXnTlYrDgOVZyKFJTU33GjBkHlC1YsIDOnTvHKSI5kumzJyIiUnn8ZdwPjPxqBa9c15tTOh79nbunHk57GukXERERESlHvlyykZFfrWBo39b079C4VNpU0i8iIiIiUk5k7Mpk2JjZtG1cm+GDSm8toxbyioiIiIiUE38eN48N2/cy9qa+1Kx28Fbnh0oj/SIiIiIi5cD4OWt4b9YafnNae5Jb1ivVtpX0i4iIiIjE2fpte/jTO/NIblmPmwe2L/X2lfSLiIiIiMSRuzNszBz2ZmXz+GXJJCaUfoqupF9EREREJI5e/fpHpixO565zOtO2cVJM+lDSX0m98847mNkBD9dasWIFNWvWJCUlhS5dunDttdeSmZkJwOTJk/Me0jVy5EjMjE8//fSg9saMGZNXlp6eTmJiIv/5z38O6NvdOe200/Ke1PuLX/yCo48+mq5duxYa75QpU+jRowdVq1Y9oI/8Cmvr97//PZ999lmB5wwdOpQ2bdqQkpJCjx49mDZtWqHtF0fr1q3ZuHEjEDyBOJqRI0eyZs2avNfXX3898+fPP6z+RUREpPJYnr6Dv05cQP8OjRjS59iY9aOkv5IaNWoU/fr1Y/To0QeUt2vXjlmzZjF37lzS0tJ48803Czy/W7dujBo1Ku/16NGjSU5OPqDOW2+9RZ8+fQ6oBzBx4kSSk5M56qijgCDp/uCDD6LG26pVK0aOHMlVV10VtV5hbf3mN7/h4YcfLvS8Rx55hFmzZvHwww9z4403HnQ8Kysrar+F+eqrr6Iez5/0P//883Tp0uWQ+hIREZHKJSs7h9vfnE31qgk8ckkyZhazvpT0V0I7duxg6tSpvPDCCwcl/bkSEhLo3bs3q1evLvB4//79+eabb8jMzGTHjh0sXbqUlJSUA+qMGjWKf/zjH6SlpR3QzmuvvcYFF1yQ9/qUU06hQYMGUWNu3bo13bt3p0qV6B/Jwto69thj2bRpE+vWrSvy/KVLlwIwYMAA7rrrLk499VSefPJJ0tPTufjii+nVqxe9evVi6tSpAGzatImzzjqLE044gRtvvJHIp1gnJe3/Cu7vf/873bp1Izk5mTvvvJMxY8YwY8YMrr76alJSUti9ezcDBgwg9ynOo0aNolu3bnTt2pXhw4cf0Oaf/vQnkpOT6dOnD+vXrweCm6yuXbuSnJzMKaecEvU6RUREpPz71+RlzF61lQcu7EqTujVi2pf26Y+lSXfCurml22aTbnB24SPaAO+++y6DBg2iY8eONGjQgJkzZ9KjR48D6uzZs4fp06fz5JNPFtiGmXHGGWfw4YcfkpGRweDBg/nf//6Xd3zVqlWsW7eO3r17c9lll/HGG29wxx13ADB16tSDpvyUhR49ejB16lQuvvjiQuu8//77dOvWLe/11q1b+fzzzwG46qqruP322+nXrx8rV67kJz/5CQsWLODee++lX79+/PnPf2bChAk8++yzB7U7adIk3n33XaZPn06tWrXYvHkzDRo04KmnnuLRRx8lNfXAJ2evWbOG4cOH891331G/fn3OOuss3n33XS688EJ27txJnz59+Otf/8of/vAHnnvuOe6++27uu+8+PvzwQ5o3b87WrVtL6V0TERGReJiTtpURny5hcHIzzk9uFvP+NNJfCY0aNYorrrgCgCuuuOKA6TfLli0jJSWFhg0b0qpVK7p3715oO1dccQWjR49m9OjRXHnllQccGz16NJdddlmBfWzevJk6deqU5iUVy9FHH33AVJpIw4YNIyUlhWeffZYXXnghr/zyyy/P+/2TTz7hlltuISUlhcGDB7Nt2za2b9/OlClTuOaaawA499xzqV+//kHtf/LJJ/z85z+nVq1aAEV+s/Htt98yYMAAGjduTNWqVbn66quZMmUKANWqVctbX9GzZ09WrFgBwMknn8zQoUN57rnnyM7OLua7IiIiIuXNnsxsbn9jFo2SqnP/BYWveSxNGumPpSJG5GNh06ZNfPbZZ8ybNw8zIzs7GzPj73//O7B/Tv/atWsZMGAA48aNY/DgwQW21bt3b+bNm0fNmjXp2LHjAcdGjRrF+vXree2114Bg5HrJkiV06NCBqlWrkpOTU+RUndK2Z88eatasWeCxRx55hEsuueSg8tq1a+f9npOTw7Rp0wpso6g5du5eonl4kVOE8ktMTMxrKyEhIW+9wTPPPMP06dOZMGECKSkpzJo1i4YNGxa7TxERESkfHp60kGXpO3nlut7UrZVYJn1qpL+SGTNmDNdeey0//vgjK1asYNWqVbRp04Yvv/zygHpNmzbl4Ycf5qGHHora3kMPPcSDDz54QNmiRYvYuXMnq1evZsWKFaxYsYI//vGPeesHjjvuOJYvX15krE899RRPPfVUkfU6depUZB2AxYsXR90hqChnnXXWAfHMmjULCNYB5N7cTJo0iS1bthR47osvvsiuXbuA4NsOgDp16rB9+/aD6p944ol8/vnnbNy4kezsbEaNGsWpp54aNb5ly5Zx4oknct9999GoUSNWrVp1aBcqIiIicfPlko2M/GoFQ/u2pn+HxmXWr5L+SmbUqFH89Kc/PaDs4osv5vXXXz+o7oUXXsiuXbv44osvCm3v7LPPZuDAgcXqI3eKz7nnnsvkyZPzjl155ZWcdNJJLFq0iBYtWuRNr1m4cGHeSPW3335LixYteOutt7jxxhs5/vjjAdi4ceMBo+KFtZWZmcnSpUsPmjtfEiNGjGDGjBl0796dLl268MwzzwBwzz335G0p+tFHH9GqVauDzh00aBCDBw8mNTWVlJQUHn30USDYbehXv/pV3kLeXE2bNuWhhx5i4MCBJCcn06NHjwMWPxdk2LBheQt/TznllIN2UxIREZHyLWNXJsPGzKZt49oMH1S8Qc3SYtGmGUh0qampnrsTS64FCxbQuXPnOEVUPqxdu5Zrr72Wjz/+OGq98847j7Fjx1KtWrVC64wfP57ly5dz6623Rm3rnXfeYebMmdx///2HFHNloM+eiIhI+fbb0d8zfs5axt7Ul+SW9Yp9npl95+6HPrKJ5vRLDDRt2pRf/vKXbNu2LW+v/oKMHz++yLZyF7QWJSsri9/97nfFjlFERESkLI2fs4b3Zq3htjM6lCjhLy1K+iUmcnf2KSuXXnppmfYnIiIiUlzrt+3hT+/MI7llPW4e2D4uMWhOfwxoypSUNX3mREREyid3Z9iYOezNyubxy5JJTIhP+q2kv5TVqFGDTZs2KQmTMuPubNq0iRo1YvskPxERESm5V6evZMridO46pzNtGyfFLQ5N7yllLVq0IC0tjfT09HiHIkeQGjVq0KJFi3iHISIiIhGWp+/grxPm079DI4b0OTausSjpL2WJiYm0adMm3mGIiIiISBxlZedw+5uzqV41gUcuSS7RQzxjQUm/iIiIiEgp+9fkZcxetZV/XnkCTerGfwqu5vSLiIiIiJSiOWlbGfHpEgYnN+P85GbxDgdQ0i8iIiIiUmr2ZGZz+xuzaJRUnfsv6BrvcPJoeo+IiIiISCl5eNJClqXv5JXrelO3VmK8w8mjkX4RERERkVLw5ZKNjPxqBUP7tqZ/h8bxDucASvpFRERERA5Txu5Mho2ZTdvGtRk+qFO8wzmIpveIiIiIiByme96bx4btexl7U19qVkuIdzgH0Ui/iIiIiMhhGD9nDe/OWsNvTmtPcst68Q6nQEr6RUREREQO0fpte/jTO/NIblmPmwe2j3c4hVLSLyIiIiJyCNydYWPmsDcrm8cvSyYxofym1uU3MhERERGRcuzV6SuZsjidu87pTNvGSfEOJyol/SIiIiIiJbQ8fQd/nTCf/h0aMaTPsfEOp0hK+kVERERESiArO4fb35xN9aoJPHJJMmYW75CKpC07RURERERK4F+TlzF71Vb+eeUJNKlbI97hFItG+kVEREREimluWgYjPl3C4ORmnJ/cLN7hFJuSfhERERGRYtiTmc1tb3xPo6Tq3H9B13iHUyKa3iMiIiIiUgwPT1rIsvSdvHJdb+rWSox3OCWikX4RERERkSJ8uWQjI79awdC+renfoXG8wymxmCX9ZtbSzP5rZgvM7Acz+20BdU4xs5lmlmVml+Q7lm1ms8KfcRHlbcxsupktMbM3zKxaAe2amY0ws6VmNsfMekQc+1l47hIz+1lEeU8zmxueM8IqwjJsEREREYm5jN2ZDBszm7aNazN8UKd4h3NIYjnSnwX8zt07A32Am82sS746K4GhwOsFnL/b3VPCn8ER5X8DHnf3DsAW4LoCzj0b6BD+3AD8G8DMGgD3ACcCvYF7zKx+eM6/w7q55w0q2eWKiIiISGV0z3vz2LB9L49flkLNagnxDueQxCzpd/e17j4z/H07sABonq/OCnefA+QUp81w9P00YExY9P+ACwuoegHwsge+BuqZWVPgJ8DH7r7Z3bcAHwODwmNHufs0d3fg5ULaFREREZEjyPg5a3h31hp+c1p7klvWi3c4h6xM5vSbWWvgBGB6CU6rYWYzzOxrM8tNwBsCW909K3ydRr4biVBzYFXE69x60crTCigXERERkSPU+m17+NM780huWY+bB7aPdziHJea795hZEvA2cJu7byvBqa3cfY2ZtQU+M7O5QEHne0HdFlKvpOUHN2x2A8E0IFq1alVQFRERERGp4NydYWPmsDcrm8cvSyYxoWLvfxPT6M0skSDhf83dx5bkXHdfE/67HJhM8E3BRoKpOrk3Ky2ANQWcnga0jHidWy9aeYsCyguK61l3T3X31MaNK97KbREREREp2qvTVzJlcTp3ndOZto2T4h3OYYvl7j0GvAAscPfHIspvMbNbiji3vplVD39vBJwMzA/n2/8XyN3p52fAe2G9n5rZQ2H5OODacBefPkCGu68FPgTOCtuvD5wFfBge225mfcK4r81tV0RERESOLMvTd/DghAX079CIIX2OjXc4pSKWI/0nA0OA0yK23jwH6ARsAjCzXmaWBlwK/MfMfgjP7QzMMLPZBEn+w+4+Pzw2HLh1JVT/AAAgAElEQVTDzJYSzPF/ISxvx/7pPxOB5cBS4Dng1wDuvhm4H/g2/LkvLAO4CXg+PGcZMKk03wwRERERKf+ysnO4/c3ZVKtahUcuSaay7OJuweB5GXZoNh64yN33lXK7rwK3u3t6abYbTWpqqs+YMaOsuhMRERGRGBvx6RIe+3gx/7zyBM5PbhbvcAAws+/cPfVw2oj5Qt783P28GLV7TSzaFREREZEjw9y0DEZ8uoTByc3KTcJfWir2MmQRERERkVKwJzOb2974nkZJ1bn/gq7xDqfUlflIv4iIiIhIefPwpIUsS9/JK9f1pm6txHiHU+o00i8iIiIiR7Qvl2xk5FcrGNq3Nf07VM4t2ZX0i4iIiMgRK2N3JsPGzKZt49oMH9Qp3uHEjKb3iIiIiMgR65735rFh+17G3tSXmtUS4h1OzGikX0RERESOSOPnrOHdWWv4zWntSW5ZL97hxJSSfhERERE54qzftoc/vTOP5Jb1uHlg+3iHE3NK+kVERETkiOLuDBszh71Z2Tx+WTKJCZU/Ja78VygiIiIiEuHV6SuZsjidu87pTNvGSfEOp0wo6RcRERGRI8by9B08OGEB/Ts0YkifY+MdTplR0i8iIiIiR4Ss7Bxuf3M21apW4ZFLkjGzeIdUZrRlp4iIiIgcEf41eRmzV23ln1eeQJO6NeIdTpnSSL+IiIiIVHpz0zIY8ekSBic34/zkZvEOp8wp6RcRERGRSm1PZja3vfE9jZKqc/8FXeMdTlxoeo+IiIiIVGoPT1rIsvSdvHJdb+rWSox3OHGhkX4RERERqbS+XLKRkV+tYGjf1vTv0Dje4cSNkn4RERERqZQydmcybMxs2jauzfBBneIdTlxpeo+IiIiIVEr3vDePDdv3MvamvtSslhDvcOJKI/0iIiIiUumMn7OGd2et4TentSe5Zb14hxN3SvpFREREpFJZv20Pf3pnHskt63HzwPbxDqdcUNIvIiIiIpWGuzNszBz2ZmXz+GXJJCYo3QUl/SIiIiJSibw6fSVTFqdz1zmdads4Kd7hlBtK+kVERESkUlievoMHJyygf4dGDOlzbLzDKVeU9IuIiIhIhZeVncPtb86mWtUqPHJJMmYW75DKFW3ZKSIiIlIBZezKZNzs1TRMqk67xkkc27AWNRKP3G0p/zV5GbNXbeWfV55Ak7o14h1OuaOkX0RERKSC2bprH9e8MJ15q7fllVUxaNmgFu0aJ9Guce3g36OTaNc4iQa1q8Ux2tibm5bBiE+XMDi5GecnN4t3OOWSkn4RERGRCiQ34V+8bgfPXNOTFvVrsix9B8vSdwb/btjBl0s3si8rJ++c+rUSaR/eAAQ3A8FNQYv6tUioUrGnwezJzOa2N76nUVJ17r+ga7zDKbeU9IuIiIhUEJEJ/3+G9GRgp6MB6Nq87gH1snOcNVt3s3TDjvCGYAfLNuzk4/nrGb1zVV69aglVaNOodt5NQO5P28a1qV29YqSJf/tgIcvSd/LKdb2pWysx3uGUWxXjrykiIiJyhCss4S9IQhWjZYNatGxQ66B6W3buY/nG4CYg94ZgwdrtfDBvHTm+v16zujXypgdFThc6uk71crNI9sslG3lp6gqG9m1N/w6N4x1OuaakX0RERKScK0nCX5T6tavRs3YDeh7b4IDyvVnZrNy0K2+qUO63BG/NWMXOfdl59ZKqV823ZqB2uJC4NtWqlt3GkBm7Mxk2ZjZtG9dm+KBOZdZvRaWkX0RERKQcK82EP5rqVRPocEwdOhxT54Byd2f9tr0R04SCm4Jpyzcx9vvVefUSqhitchcSR0wXat84KSbTbu55bx4btu9l7E19qVmtEu9alJFWKs0o6RcREREpp8oq4Y/GzGhStwZN6tbg5PaNDji2Y28W/0vfP01oWfoOlm7YwZTF6ezL3r+QuFFSNdo2jpgqdHRwM9C8Xk2qHMJC4vFz1vDurDXcdkYHklvWO+xrLFfcYcN8WDgRFo6HtbNKpVkl/SIiIiLlUHlI+IuSVL0q3VrUpVuLAxcSZ2XnkLZl9wGLiJel72DSvLVs3ZWZV6961SrhzcCB04XaNkoqdPR+/bY9/OmdeSS3rMfNA9vH9PrKTE42rJoOCycEif6WFUF5i95wxl/g3jsOuwsl/SIiIiLlTEVI+KOpmlCF1o1q07pRbU7vfMwBxzbv3BcxTSiYKjR3dQYT5649YCFx83o1D1gzkPstwR/GzGFvVjaPX5ZMYkLZrSEodZm7Ydl/YdEEWDQJdm2ChGrQ5lQ4+TY47myo0ySsrKRfREREpFKp6Al/URrUrkaD2g3o1frAhcR7MrP5cdOuA7cZTd/Bt//bzO7M7APq3nfB8bRtnFSWYZeOXZth8YfBaP6yzyBzF1SvCx3Pgk7nQvszoHqdots5BEr6RURERMqJjF2ZlTrhj6ZGYgLHNanDcU0OTHpzcpx12/bkfTuQ4zCkz7FxivIQbPkRFk0Mpu78+BV4NtRpBilXBYn+sf2gauyfmKykX0RERKQcyNiVydUvfH1EJvzRVKliNKtXk2b1alaMvfjdYf28/fPz180Nyht3hn63B4l+sxOgjJ91oKRfREREJM6U8Fdw2VmwclqY6E+AjJWAQas+cOb9QaLfsF1cQ1TSLyIiIhJHSvgrqH07g3n5CyfA4g9g9xZIqA7tBsKpw6DjIEgqP39LJf0iIiIicaKEv4LZuTFI8BdOCBL+rD1Qo16Q4Hc6B9qdDtXL5wJjJf0iIiIicaCEv4LY/L/903ZWfQ2eA0e1gB4/Cxfi9oWE0n/icGlT0i8iIiJSxpTwl2PusHb2/kR/ww9B+TFd4ZRhQaLfpHuZL8Q9XCVK+s2sPtDS3efEKB4RERGRSi0y4X9mSA8l/OVBdib8ODVM9CfCtjSwKtCqL/zkQTjuHGjQJt5RHpYik34zmwwMDuvOAtLN7HN3P/xHg4mIiIgcQfIn/Kd1OqbokyQ29u6ApZ8Eif6SD2FPBlStCe1Og4F3BfP0azeMd5Slpjgj/XXdfZuZXQ+85O73mJlG+kVERERKQAl/ObBjAyyaFCT6yydD9l6o2QA6nRdM22k7EKrVineUMVGcpL+qmTUFLgP+FON4RERERCodJfxxtGlZ8JCshRNg1TeAQ71W0Ou6INFv2QcSKv8y1+Jc4b3Ah8CX7v6tmbUFlsQ2LBEREZHKIWNXJte8MF0Jf1nJyYE138OicCFu+sKgvEl3GPDHINE/5vgKtxD3cEVN+s0sgWDhbvfcMndfDlwc68BEREREKrrchH/Ruu1K+GMpax+s+CJI8hdNhO1rwRKg9cnQ8+fBHvr1WsU7yriqEu2gu2cTLOItMTNraWb/NbMFZvaDmf22gDqnmNlMM8sys0sKOH6Uma02s6ciynqa2VwzW2pmI8wOvk0zs+pm9kZYZ7qZtY449sewfJGZ/SSifFBYttTM7jyUaxYRERHJpYQ/xvZsg3lvw5hfwCPt4NWLYPYoaJEKP/0PDFsKP3sf+vzqiE/4oXjTe74Kk+43gJ25he4+s4jzsoDfuftMM6sDfGdmH7v7/Ig6K4GhwO8LaeN+4PN8Zf8GbgC+BiYCg4BJ+epcB2xx9/ZmdgXwN+ByM+sCXAEcDzQDPjGzjuE5TwNnAmnAt2Y2Ll+sIiIiIsWihD9Gtq8LRvIXToDln0NOJtRqBF0uCBfiDoDEmvGOslwqTtLfN/z3vogyB06LdpK7rwXWhr9vN7MFQHNgfkSdFQBmlpP/fDPrCRwDfACkhmVNgaPcfVr4+mXgQg5O+i8A/hL+PgZ4KvxG4AJgtLvvBf5nZkuB3mG9peHUJcxsdFhXSb+IiIiUiBL+Upa+eP/8/LRvg7L6beDEG4Ndd1r2hioJ8Y2xAigy6Xf3gYfbSTi95gRgejHrVwH+AQwBTo841JxgJD5XWliWX3NgFYC7Z5lZBtAwLP+6kPNX5Ss/sTixioiIiORSwl8KcnJg9Xf7d9zZFO4f0+wEGHh3MD//6C5H3ELcw1Ws/YnM7FyCKTE1csvc/b7Czzjg3CTgbeA2d99WzLh+DUx091X5puwX9Nf1grotpF5h5QWtbSioXczsBoLpRbRqpflhIiIiElDCfxiy9sGKKfufiLtjHVSpCq37BSP6x50NdVvEO8oKrThP5H0GqAUMBJ4HLgG+KU7jZpZIkPC/5u5jSxDXSUB/M/s1kARUM7MdwJNA5F+8BbCmgPPTgJZAmplVBeoCmyPKCzq/sPIDuPuzwLMAqampBd4YiIiIyJFFCf8h2JMBSz4OEv2ln8DebZBYGzqcEUzb6XAm1Kwf7ygrjWLN6Xf37mY2x93vNbN/AEUm8OEc+heABe7+WET5LQDu/lRh57r71RH1hwKp7n5n+Hq7mfUhmCp0LfDPAtodB/wMmEZwk/KZu7uZjQNeN7PHCBbydiC4gTGgg5m1AVYTLPa9qhjvjYiIiBzhlPCXwLa1+xfi/m/K/oW4x18YJPptToXEGkW3IyVWnKR/d/jvLjNrBmwC2hTjvJMJ5uTPNbNZYdldQCdgKoCZ9QLeAeoD55vZve5+fBHt3gSMBGoSLODNXcSb1y7BzcYr4ULdzQRJPO7+g5m9SbBANwu4OdyWNPem4UMgAXjR3X8oxjWKiIjIEUwJfzGkL94/P3/1jKCsfptgK81O50GLXlqIWwbMPfoMFTP7P4LR9NMJtrV04Hl3/79D6tBsPHCRu+87lPPLut1oUlNTfcaMGWXVnYiIiJQjGbsyGfLidBauVcJ/gGgLcTudGyT6jTtpIW4JmNl37p56WG0UlfTn67A6UMPdMw6n08pCSb+IiMiRKTLh//c1PTi98xGe8Gfthf99EST6iybCjvX7F+J2Ok8LcQ9TaST9hU7vMbOLohyjhAtzRURERCoFJfyhyIW4Sz6Gfdu1ELccizan//wox5xiLOYVERERqUyO+IS/oIW4tRtD159qIW45V2jS7+4/L8tARERERMqzIzbh10LcSiHa9J47op0YuQ2niIiISGV2RCX8hS7E7QGn3a2FuBVUtOk9dcosChEREZFy6ohI+AtdiNs/fCLuOVC3ebyjlMMQbXrPvWUZiIiIiEh5U6kT/oIW4lZLgvaRC3HrxTtKKSVFPpzLzFoQ7NN/MsEC3i+B37p7WoxjExEREYmbSpnwF7oQ96JwIe4pWohbSRXnibwvAa8Dl4avrwnLzoxVUCIiIiLxlLG7EiX8BS3EbdAW+twULsRN1ULcI0Bxkv7G7v5SxOuRZnZbrAISERERiaeM3ZkMeaECJ/xRF+L+X7gQ9zgtxD3CFCfp32hm1wCjwtdXAptiF5KIiIhIfFTYhF8LcaUIxUn6fwE8BTxOMKf/q7BMREREpNKocAm/FuJKCRSZ9Lv7SmBwGcQiIiIiEhcVJuHfvi5I8rUQV0ooatJvZgOB3wDHhUULgKfcfXKM4xIREREpE+U+4d+4ZP/8/LRvg7K8hbjn6om4UizRnsh7LsG0nvuAewEDegAvmtkt7j6xbEIUERERiY3chH/B2m08c03P8pHw5+TAmpn7E/2Ni4PyZidoIa4csmgj/cOAC919dkTZLDObQbBvv5J+ERERqbDKVcKftQ9WfBEk+Ysmwva14ULcftD7BjjubKjbIn7xSYUXLelvki/hB8Dd55hZObgNFhERETk05SLh37s9YiHuR7B3GyTWhvanQ+fzw4W49cs+LqmUoiX9Ow/xmIiIiEi5FdeEf8eG/U/EXT4ZsvdBrUbQ5YJg2k7bUyGxZtnFI0eMaEl/OzMbV0C5AW1jFI+IiIhIzMQl4d+0bP/8/FXfAA71jg2m7XQ6F1qeqIW4EnPRkv4Lohx7tLQDEREREYmljN2ZXFsWCb87rPl+/9aa6QuC8qbJMPCuINE/uosW4kqZKjTpd/fPyzIQERERkVjJTfjnxyrhz86EFV/uX4i7bTVYAhzbF3r+DTqdA/ValW6fIiVQnCfyioiIiFRYMUv49+6AZZ8Gif7iD4In5FatGSzEPe1u6DgIajUonb5EDpOSfhEREam0Sj3h37lx/0LcZf+F7L1Qs0GwCLfTudB2IFSrVTrBi5QiJf0iIiJSKZVawr/5f/vn56/6GjwH6raC1F8EiX6rkyBBKZWUb9GeyJsAXA+0AD5w96kRx+529wfKID4RERGREjushN8d1s0JkvwF42HDD0H5MV3hlD8EiX6TblqIKxVKtNvS/wC1gG+AEWb2ubvfER67CFDSLyIiIuXOISX82Vmw8qv9I/oZq8CqBKP4P3kQjjsHGrSJffAiMRIt6e/t7t0BzOwp4F9mNha4kmCvfhEREZFypUQJ/75dsOyzcCHuJNi9BRKqQ7vTYMCdwULc2o3KLniRGIqW9FfL/cXds4AbzOzPwGdAUqwDExERESmJYiX8OzcFO+0snBAk/Fm7oUZd6Hh2MG2n3WlQXWmOVD7Rkv4ZZjbI3T/ILXD3+8xsDfDv2IcmIiIiUjzrMvZw4yszCk74t/y4f8edH6cGC3GPag49hgSJ/rEnQ0Ji/IIXKQPRHs51TSHlzwPPxywiERERkWJyd96euZp73/+BzOwc/n11T07vdDSsmxvOzx8f/A7BU3D7/y5I9JumaCGuHFEOaX8pMzvT3T8u7WBEREREimv9tj3cNXYuny7cwInH1uWJvntpuvJJ+Gg8bP0RMGh5Ipx5f5DoN2wX75BF4uZQN5V9AdCzpEVERKTMuTvvfL+ah8Z9T2r2bD5qu4QOW7/A3tkECdWg7QDof0ew407S0fEOV6RciLZP/7jCDgENYxOOiIiISOHSN6zjvbdeotm6z5hSdQ41E/bApqOgw1nBaH6HM6F6nXiHKVLuRBvp7w9cA+zIV25A75hFJCIiIhIpYzW+cALpM8ZSP/0briebnTUbUb3bVdD5PGjdH6pWK7odkSNYtKT/a2CXu3+e/4CZLYpdSCIiInJEc4eNi2HB+8Fi3DUzMWB7TlO+TLqI3mcPocXx/aFKlXhHKlJhRNu95+wox06JTTgiIiJyRMrJgdXfBbvtLBwPm5YCsKV+N16xq5iU2ZOLzjqNX/RrQ0IV7bojUlJFLuQ1s2OA5oADa9x9fcyjEhERkcovax+smBJurTkRdqyDKlWhdT+2p1zPA0tb88aiHE5oVY9/XpJM+6P10CyRQxVtIe8JBA/hqgusDotbmNlW4NfuPrMM4hMREZHKZO92WPJxkOgv+Qj2boPE2tD+dOh8Pt7+TMYv2c2f35vHzn3Z/PHsTlzfv61G90UOU7SR/peAG919emShmfUJjyXHMjARERGpJHZsgEWTgmk7yydD9j6o1RC6DIZO50PbUyGxJht37OX/xs5j0rx1JLesxz8u7U77o7UTj0hpiJb0186f8AO4+9dmVjuGMYmIiEhFt3l5OG1nAqz8GnCo1wp6/TLYWrNVH6iSkFd9wpy1/N9789ixJ4vhgzrxy/5tqJqghboipSVa0j/JzCYALwOrwrKWwLXAB7EOTERERCoQd1g7O0z0x8OG+UF5k24w4M4g0T+mK9iB03Q27djLn9/7gQlz19K9RV0evTSZjsdodF+ktEXbvedWMzsbuIBgIa8BacDT7j6xjOITERGR8io7C1ZOC3fcmQAZq8CqQKuT4CcPQadzoH7rQk+fNHctd787j217Mhn2k+O48ZS2Gt0XiZGou/e4+yRgUhnFIiIiIuXdvl2w/L+wYDwsngS7t0BCdWh3WjCi33EQ1G4UtYnNO/fx5/fmMX7OWro1r8vrl/bhuCYa3ReJpWi79yQA1wMtgEnu/lXEsbvd/YEyiE9ERETibddmWPxhMKK/9FPI2g016gYJfqdzod3pUL1422l+MG8dd787l4zdmfz+rI7ceGo7EjW6LxJz0Ub6/wPUAr4B/mlmn7v7HeGxiwAl/SIiIpVVRtr++fkrpoJnQ51mcMI1QaLfuh8kJBa7uS0793HPuB8YN3sNxzc7ileuO5HOTY+K4QWISKRoSX9vd+8OYGZPAf8ys7HAlQTz+0VERKSycIf0hcG0nYXjYe2soLzRcdDvtiDRb9bjoIW4xfHRD+u46515bN21jzvO7MhNAzS6L1LWoiX91XJ/cfcs4AYz+zPwGaBH4omIiFR0OTmQ9m24EHd8sM0mQItecMa9QaLfqMMhN7911z7+Mu4H3p21hi5Nj+LlX/SmSzON7ovEQ7Skf4aZDXL3vO053f0+M1tD8KReERERqWiy9sL/poSJ/kTYuQGqJEKbU+CkW4JEv06Tw+7m4/nrueuduWzZuY/bzujAzQPba3RfJI6ibdl5TSHlzwPPxywiERERKV17tsGSj4I5+ks+hn3boVoSdDgTOp0X/Fujbql0lbErk3vf/4Gx36+mU5M6jPx5L45vVjpti8ihi7plp4iIiFRQ29fDoonBiP7yzyEnE2o3hq4XBYl+21OhavVS7fLTBev549i5bNq5j1tP78AtA9tTrapG90XKg5gl/WbWkuBpvk2AHOBZd38yX51TgCeA7sAV7j4mLD8WGAskAInAP939mfBYT2AkUBOYCPzW3T1fu9XDvnsCm4DL3X1FeOyPwHVANnCru38Ylg8Cngz7fN7dHy7Ft0NERCT2Ni0LkvwF44O5+jjUbwN9fhUk+i16QZWEUu82Y3cm970/n7dnptGpSR1eHNqLrs01ui9SnsRypD8L+J27zzSzOsB3Zvaxu8+PqLMSGAr8Pt+5a4G+7r7XzJKAeWY2zt1z1xPcAHxNkPQP4uAHiF0HbHH39mZ2BfA34HIz6wJcARwPNAM+MbOO4TlPA2cSPHX427C/+YiIiJRX7sEuOwsnBIl++oKgvGkyDLwrSPSP7nxIO+4U138XbuDOsXPYuGMfvzmtPb85rYNG90XKoWgP5+oR7UR3n1nE8bUEyTvuvt3MFgDNgfkRdVaEfeXkO3dfxMvqQJWwXlPgKHefFr5+GbiQg5P+C4C/hL+PAZ4yMwvLR7v7XuB/ZrYU6B3WW+ruy8N2R4d1lfSLiEj5kp0FK78K99CfABmrwKrAsSdDz4eDhbj1WsU8jIzdmTwwfj5vfZdGx2OSeO7aVLq3qBfzfkXk0EQb6f9H+G8NIBWYTbA/f3dgOtCvuJ2YWWvghPC84p7TEpgAtAeGufsaM0slGInPlUZwI5Ffc2AVBNuNmlkG0DAs/7qQ81flKz+xkLhuIPimgVatYv8/qiIiImTuhmWfBaP5iyfB7i1QtQa0Ow0G/DF4Mm7thmUWzuRFG7jz7bmk79jLzQPbcevpHahetfSnDYlI6Ym2e89AyBv1vsHd54avu3LwdJxChdNz3gZuc/dtxT3P3VcB3c2sGfCumY2h4IeCeQFlhdUrrLyg7yELahd3fxZ4FiA1NbXAOiIiIodt9xZY/CEseD9I+DN3BTvsdBwUTNtpfzpUq12mIW3bE4zuvzkjjQ5HJ/GfIT1JbqnRfZGKoDhz+jvlJvwA7j7PzFKK07iZJRIk/K+5+9hDCTAc4f8B6A9MBVpEHG4BrCngtDSgJZBmZlWBusDmiPKCzi+sXEREpGxkrA523FnwPqz4Ejwb6jSFlKuCRL91P0hIjEtoUxanM/ztOazftoebBrTjt6d3oEaiRvdFKoriJP0LzOx54FWC0e9rgAVFnRTOoX8BWODuj0WU3wLg7k9FObcFsMndd5tZfeBk4DF3X2tm282sD8FUoWuBfxbQ7jjgZ8A04BLgM3d3MxsHvG5mjxEs5O0AfEPwDUAHM2sDrCZY7HtVMd4bERGRw5O+aP+OO2vC5XKNOsLJt0Kn86HZCVAlfgtjt+/J5K8TFjD621W0a1ybsb8+mRSN7otUOMVJ+n8O3AT8Nnw9heI9kfdkYAgw18xmhWV3AZ0IRuwxs17AO0B94Hwzu9fdjwc6A/8ws9wpOY9GfNtwE/u37JzE/kW8ee0S3Gy8Ei7U3UyQxOPuP5jZmwQLdLOAm909O4zlFuBDgi07X3T3H4pxjSIiIiWTkxMk9wveDxbibloSlDfvCaffE4zoN+4YvY0y8sWSdIaPmcO6bXu48dS23H5GR43ui1RQlm+L+4IrmdUEWrn7osPu0Gw8cFG+HXoOW6zajSY1NdVnzJhRVt2JiEhFlbUPfvwyGM1fNBG2r4UqVYPpOp3Og+POgboF7UsRHzv2ZvHXCQsY9c1K2jauzaOXJtOjVf14hyVyxDKz79w99XDaKHKk38wGA48A1YA24Xz++9x98KF06O7nHcp58WpXRETkkOzdAcs+DXfc+RD2ZkBiLWh/RpDodzwLapa/RHrq0o38Ycwc1mTs5oZT2nLHmRrdF6kMijO95x6CvewnA7j7rHALThEREYm0c1OwpeaC8bD8v5C1B2o2gM7nB/vntxsIiTXjHWWBduzN4qGJC3ht+kraNqrNmF+dRM9jG8Q7LBEpJcVJ+rPcPcNi+DQ/ERGRCmvLj/sflLXyK/AcqNsSev4cOp8HLftAQnH+7zZ+vloWjO6v3rqb6/u14fc/OU6j+yKVTHH+V2iemV0FJJhZB+BW4KvYhiUiIlJOucOG+cFo/sLxsG5OUH708dD/90Gi36Q7VIDBsp17s3h40kJe+f/t3Xd8VfX9x/HXJwsIIxD2JuwhygbRqqAiImgdrbtuW+uqVmut3cPaYaut9WcddVQEtwUEBQdOhmyBhL03BEKAzHu/vz/OCQkIIZDce3Jv3s/Hg0duvufck8/J5eZ+zvd8v5/vzHV0aJzK698/lQEd1LsvEo8qkvTfCTwEFADj8Crc/C6SQYmIiFQr4RBs/Kq04s7uNYBB28Fw7u+8oTuNOwUd5XGZsWoXP3lzIRt353HjaRncf1436qSod18kXh0z6XfOHcBL+h+KfDgiIiLVRHEBrP7E681fNhn274DEFMg4E06726u4U7950FEetwOFxfxpShYvzlhH+8apvHrrqQzKUO++SLyrSPWersB9QIey+zvnhkcuLBERkQDk74UVU73e/PBJNZMAACAASURBVBXToDAXUupDl3O9YTudz4XaDYKO8oTNWr2L+99YxPrsA1w/tAM/GdmN1JTqPd9ARKpGRd7prwNPAc8CociGIyIiEmX7tpdOxF3zCYQKoW5TOOkSr+pOxhmQVCvoKCvlQGExf35vGS98uZZ26amMv3UIQzo2DjosEYmiilbvqcgKvCIiIrEhe3XpRNwNswEHjTrAoFu9RL/NQEiIj/Hts9dkc/8bC1m36wDXndqeB87vrt59kRqoIu/6iWb2Q+BtvMm8ADjnsiMWlYiISFVyDrYs9Hv0J3nVd8CrsjPsZ95E3GY9Y6LiTkXlFYb4y/vLeP7LNbRuWIdxtwzh1E7q3RepqSqS9F/nf72/TJsDOlZ9OCIiIlUkVAwbZvo9+u9CznqwBGg3FEY+4k3EbdQ+6CgjYtHGPfxo/AJW79zPtUPa89Pzu1O3lnr3RWqyilTvyYhGICIiIpVWlO+thJs5yVsZ98AuSKwFnYbDmT+BbudD3SZBRxkx4bDj6c9W89f3l9G0fi1euXkwQzvH7/mKSMUdNek3s+HOuY/M7JIjbXfOvRW5sERERCooPweWT4WsibDiAyjaD7XSoOsI6D4aOp8DteoFHWXEbd+bz72vLeTzlTsZ2asFj1zam4apKUGHJSLVRHk9/WcCHwFjjrDNAUr6RUQkGLlbS8fnr/kMwkVQrzmccrmX6Hf4FiTVnIT3w8xt3P/GIg4UFvPHS3pzxcC2WBzNTxCRyjtq0u+c+5X/9YbohSMiInIUu1Z5SX7mJG91XBykd4Qht3kVd1oPgISEoKOMqvyiEI9MyeKFL9fSo2UD/nllHzo3qx90WCJSDVVoVo+ZXQD0AmqXtDnnfhupoERERI5acaflKX7FndHQrEdcVdw5Hiu25XLnuPlkbc3lxtMy+MnIbtROjo8yoyJS9SqyIu9TQCowDG+BrsuA2RGOS0REaqJwCNbPOHrFne4XQMN2QUcZKOccY2et53eTllKvVhLPXz+QYd2bBR2WiFRzFenpH+qcO9nMFjnnfmNmj6Lx/CIiUlWK8mH1dG8i7rKyFXeG1YiKO8dj9/5CHnhzEVOXbuNbXZrw6HdPoVn92sd+oojUeBVJ+vP8rwfMrBWwC1AZTxEROXEHK+5MgpUfQOE+qNUAup7n9eZ3PgdqaWx6WTNW7eKeVxewa38BP7+gBzeelkFCQs0c2iQix68iSf8kM2sI/AWYh1e559mIRiUiIvEndxsse9cburPm09KKO72/Az1GQ4czalTFnYoqCoV57IPlPDl9FRmN6/LsdadxUuu0oMMSkRhTkcW5fuc/fNPMJgG1nXM5kQ1LRETiwq5VpRNxN8wGHDTKgCE/gO5joM3AGldx53is33WAu8bPZ8GGPXx3QBt+NaaXVtYVkRNS0eo9Q4EOJfubGc65lyIYl4iIxCLnYOsifyJumYo7LU5WxZ3j9M78Tfz8ncWYwRNX9WX0ya2CDklEYlhFqvf8F+gELABCfrMDlPSLiIhfcWeml+RnTYI9JRV3ToXz/uiN0W/UPugoY8a+gmJ++c5i3pq/iQHtG/HYFX1o0yg16LBEJMZVpKd/ANDTOeciHYyIiMSI8irunHE/dBulijsnYMGGPdw9fj4bsg9w99lduHN4Z5ISNfxJRCqvIkn/YqAFsCXCsYiISHWWnwMrpkHmxEMr7nQZ4U3EVcWdExYOO576dBV/m7qcZvVrMf7WUxmUkR50WCISR46a9JvZRLxhPPWBpWY2Gygo2e6cuzDy4YmISKD2bS+diLv6E6/iTt1m0PsybyJuhiruVNa2vfnc8+oCvly1iwt6t+Thi3uTlpocdFgiEmfK6+n/a9SiEBGR6iN7delE3CNW3BkACYlBRxkXpi3dxk/eWEh+UZg/Xdqb7w5oi2mSs4hEQHlJ/yaguXPui7KNZnaGv01EROKBc7D1ay/Jz5wE25d47S16w1kPekN3mvVUxZ0qlF8U4g/vZvLfmevo2bIB/7yqL52a1gs6LBGJY+Ul/Y8BPztC+wF/25iIRCQiIpF3zIo7o6BRh6CjjEvLtuZy17j5LNuWy82nZ3D/yG7UStKdExGJrPKS/g7OuUWHNzrn5phZh4hFJCIikVFc4FXcySypuLMTElOgo19xp+v5UK9p0FHGLeccL89cx+/fzaR+7SReuGEgZ3VrFnRYIlJDlJf01y5nW52qDkRERCKgIBdWTPWG7ayY6lXcSakPXUd4C2V1OVcVd6Ige38hP3ljER9kbuPMrk3563dOoWn9WkGHJSI1SHlJ/1dmdotz7pmyjWZ2EzA3smGJiMgJ27cDlk32K+5Mh1Ah1G0KJ10KPUoq7ijhjJYvV+7kntcWsHt/Eb8Y3ZMbhnYgIUHzI0QkuspL+n8EvG1mV1Oa5A8AUoCLIx2YiIgchz3rSyvurJ8BLgwN28HAW7xEv+0gVdyJsqJQmL9NW85Tn6wio0ldnrtuICe1Tgs6LBGpoY6a9DvntgFDzWwYcJLf/K5z7qOoRCYiIkfnHOzI8sbnZ06Erf4UrGa9vPH53Ud71XdUcScQ63bt565x81m4MYcrB7XlF6N7kppSkfUwRUQi45h/gZxzHwMfRyEWEREpTzgMm+ZC1kSvVz97ldfeZhCc+1sv0W/cKdgYhbfmbeQX7ywmMcF48up+jOrdMuiQRESOnfSLiEiAQkWw9nO/4s5kyN0CCUneuPxTb4fuF0D9FkFHKUBufhG/eGcx7yzYzKAO6fz9ij60bqi6FyJSPSjpFxGpbgoPwKoPvd785e9B/h5IToXOZ3sr4nYdAXUaBR2llDFv/W7uHj+fzXvyuffcrtw+rDOJmqwrItWIkn4Rkeogbzcse8+biLvyQyjO8xL7bqO8FXE7DoOU1KCjlMOEwo6nPlnF36Ytp0WD2rz2/SH0b58edFgiIt+gpF9EJCh7t5SuiLv2cwgXQ/1W0PcaL9FvfxokJgcdpRzF1px87nl1ATNW72L0yS35w8W9Sauj10tEqicl/SIi0bRrVWnFnU1zvLbGnWHond7QnVZ9ISEh2BjlmN5fspUH3lxEYXGYv1x2Mpf1b4OpUpKIVGNK+kVEIsk52LLQ683PnAQ7Mr32ln1g+M+9RL9pN5XWjBF5hSF+/+5Sxs5aT+/WaTx+RR86Nq0XdFgiIsekpF9EpKqFQ7B+Zmmin7MeLMEbrtP/T17FnYZtg45SjlPW1r3c+cp8Vmzfx61ndOS+Ed1ISdJdGRGJDUr6RUSqQnEBrJ7ul9acAgd2QmIt6DQMzvwJdDsf6jYJOko5Ac45Xpqxjj9MzqRB7WReunEQZ3RtGnRYIiLHRUm/iMiJKsiFFVO93vwVU6FwH6TUh67neRNxO58DteoHHaVUwq59BfzkjUV8mLWd4d2b8efLTqZJvVpBhyUictyU9IuIHI99O7xFsrImeT37oUKo2xROuhR6jPEWzUpSUhgPPl+xk3tfW8CevCJ+PaYn1w3toMm6IhKzlPSLiBzLnvVeb37WJFg/A1wYGraDgbd4iX7bQZCQGHSUUkUKi8M8Om0ZT3+6mk5N6/HijYPo0bJB0GGJiFSKkn4RkcM5BzuySktrbl3ktTfrBWfcD91HQ4veqrgTh9bs3M/d4+ezaGMOVw1uxy8u6EmdFF3QiUjsU9IvIgIQDsOmuZA10evVz17ltbcZBOf+1kv0G3cKNkaJGOccb87bxC//t5jkxASeuqYfI09qGXRYIiJVRkm/iNRcoSJvJdzMid44/dwtkJDkjcs/9XavtGb9FkFHKRG2N7+In7+9mAkLNzM4I53HruhDy7Q6QYclIlKlIpb0m1lb4CWgBRAGnnbOPX7YPmcAjwEnA1c4597w2/sA/wc0AELAH5xzr/rbMoDxQDowD7jWOVd42HENeBwYBRwArnfOzfO3XQf83N/19865F/32/sALQB1gMnC3c85V1e9DRKqJwgOw6iNvfP6yKZC/B5JTofPZ3kJZXUdAnUZBRylRMnfdbu4eP58tOfncN6Irt53VmcQEDdsSkfgTyZ7+YuDHzrl5ZlYfmGtm05xzS8vssx64HrjvsOceAL7nnFthZq38577vnNsD/An4u3NuvJk9BdyEd4FQ1vlAF//fYH/7YDNLB34FDACcf9wJzrnd/j63AjPxkv6RwJQq+U2ISLDy9vilNSfAyg+h6ADUbujVzu8xBjoOg5TUoKOUKAqFHU9+vJLHPlxBy7TavPb9U+nfXhd7IhK/Ipb0O+e2AFv8x7lmlgm0BpaW2WctgJmFD3vu8jKPN5vZdqCpmeUAw4Gr/M0vAr/mm0n/RcBLfk/9TDNraGYtgbOAac65bP/nTgNGmtl0oIFzbobf/hLwbZT0i8Su3G2w7F1vfP6aTyBcDPVaQJ+rvPH5HU6HxOSgo5QAbN6Txz2vLmDWmmwu6tOK3337JBrU1v8FEYlvURnTb2YdgL7ArBN47iAgBVgFNAb2OOeK/c0b8S4kDtca2FDm+5L9ymvfeIR2EYklu9d6SX7mRNgwC3CQ3tEfnz8GWveHhISgo5QAvbd4Cw+8+TXFoTCPfucULunXWrX3RaRGiHjSb2b1gDeBHznn9h7nc1sC/wWuc86F7ch/mY807v5o+x1v+5FiuhVvGBDt2rU70i4iEi3OwfalpYn+tq+99ha94awHvaE7zXqotKaQVxjit5OWMm72ek5uk8Y/ruhLhyZ1gw5LRCRqIpr0m1kyXsI/1jn31nE+twHwLvBz59xMv3kn0NDMkvze/jbA5iM8fSPQtsz3JfttxBviU7Z9ut/e5gj7f4Nz7mngaYABAwZooq9ItJWU1syc4E3GzV4NGLQdDCP+4FXcSc8IOkqpRrbn5vO952azbFsuPzizE/ee25WUJN3xEZGaJZLVewx4Dsh0zv2tTPsdAM65J8p5bgrwNt64/NdL2p1zzsw+Bi7Dq+BzHfA//zkXA4Occw8CE4A7zGw83kTeHOfcFjN7H3jYzEpma40AHnTOZZtZrpkNwRuC9D3gn1XyixCRyisprZk1CbLeLVNa80wYeid0uwDqNw86SqmGtu3N58pnZrI1J58XbhjEmV2bBh2SiEggItnTfxpwLfC1mS3w234GdAe+ADCzgXjJfSNgjJn9xjnXC/gucAbQ2Myu9597vXNuAfAAMN7Mfg/Mx7uwAOgElAwfmoxXrnMlXiWgGwD85P53wFf+fr8tmdQL3EZpyc4paBKvSLCK8rzSmpkTv1las8eF0GUE1GkYdJRSjW3N8RL+7XvzefHGQQzskB50SCIigbFol6I3s0nAJYfX1q+C474M3OOc21GVxy3PgAED3Jw5c6L140Ti38HSmhNh5QeHltbsPho6DVdpTamQzXvyuPKZmezaV8iLNw6kf3sl/CISu8xsrnNuQGWOEfUVeZ1zoyN03GsicVwRibB9270hO5kTYc2nEC5SaU2plE178rjy6Zns3l/ISzcNol871d8XEYl60i8icrC0ZtYkWD+Tg6U1h9zmDd1RaU05QRuyD3DlMzPZm1fEyzcP5pS2GgImIgJK+kUkGpyD7Zleb37WRNjql9ZsXlJaczQ066nSmlIp63d5Cf++gmLG3jyE3m3Sgg5JRKTaUNIvIpFRUloza6KX7B9SWvP33tAdldaUKrJ2536uemYmB4pCjL15MCe1VsIvIlKWkn6pkKyte/nvjHVcOaidPkzl6EJFsO4Lv0dfpTUlOtbs3M+VT8+koDjEKzcPoWerBkGHJCJS7Sjpl2N6c+5GHnrna/KLwoydtZ5v92nFfed1o00jVVERypTWnATLJqu0pkTVqh37uPLpmYTCjnG3DqF7CyX8IiJHoqRfjiq/KMRvJnrL1g/pmM7DF/fmjbkbee7zNUxevJUbTuvAD8/qTFodVVapcfJzYPlUb1Xcg6U106DbKJXWlKhZuT2XK56eBcD4W4fQpXn9gCMSEam+ol6nP57Ec53+DdkHuG3sXBZv2sttZ3Xix+d2JSnRq6ayeU8ej05dzlvzN9KwTjJ3Du/CNUPaa1n7eFdSWjNrEqz+pLS0ZvcLoMcYldaUqFq+LZernpmJmTHuliF0blYv6JBERCKmKur0K+mvhHhN+j/M3MY9ry7AAX/7bh/O7XnkMdhLNufwx8lZfL5yJ+0bp/KT87ozqncLTBVY4sfudV6SnzmxtLRmowwvyVdpTQlI5pa9XP3sLJITjVduGUKnpkr4RSS+KekPWLwl/cWhMH+btpwnp6/ipNYNePKq/rRrXP4QDeccnyzfwR8nZ7FsWy792jXkoQt6aPXLWOUc7MjykvzMibB1kdfevLef6Ku0pgRryeYcrnl2FrWSEhl36xAymtQNOiQRkYhT0h+weEr6d+QWcNe4+cxYvYsrB7XlV2N6UTs5scLPD4Udb8zdwKNTl7M9t4CRvVrwwPnd9YEcC5yDTfO88fmZEyF7FQdLa/YYrdKaUm0s3pTDNc/NIjXZS/jbN9bfFxGpGZT0Byxekv7Za7K545V57M0v4vff7s1l/duc8LEOFBbz7GdreOqTVRQWh7l6cDvuOrsLjevVqsKIpdJCxbD+y9JVcfdu8ktrnuEl+d1Hq7SmVCuLNu7hmmdnUb92MuNvHULbdE0UF5GaQ0l/wGI96XfO8exna3jkvSzapafy5NX96NGyasrdbc/N57EPVvDqVxtITU7ktmGduPG0jOO6eyBVrLgAVk/3evSzJkNeNiTV8UtrjoGu50GdRkFHKfINCzbs4drnZtEwNZlXblbCLyI1j5L+gMVy0r83v4j7X1/I+0u2MbJXC/78nZNpULvqK6+s3J7LI1Oy+CBzO63SavPjEd24uG9rEhI0JjwqCnJhxTSvN3/5VCjMhVoNoOtIL9HvfDakaIiEVF9z1+3m+v/MplHdFMbdOoTWDesEHZKISNQp6Q9YrCb9Szfv5Ydj57Jhdx4Pnt+dm07PiHjFnRmrdvHw5Ey+3pRDr1YN+NmoHpzWuUlEf2aNdSAblk3xxuev+ghCBVC3qVdas/sYbwhPUkrQUYoc05y12Vz//Fc0qecl/C3TlPCLSM2kpD9gsZj0vz5nAz9/ZzENU5N54qp+DOwQvSo74bBj4qLN/Pm9ZWzak8dZ3Zry4Pk96NZCC+pU2t7NXg39zAmw9gtwIUhr61fcGeNNyk3Q0CqJHbPXZHP987Np0aA2424dQvMGtYMOSUQkMEr6AxZLSX9+UYhfT1jC+K82MLRTYx6/oi9N6wczuTa/KMRLM9byxEcr2VdQzHcHtOXec7vSTB/qx2fXqtIa+hu/8tqadCtN9FueotKaEpNmrNrFjS98RauGtRl3yxD9bRCRGk9Jf8BiJelfv8tbXXfJ5r3cMawz95zblcRqMKZ+9/5Cnvh4JS/NWEtSQgK3nNGR75/Rkbq1koIOrXpyDrYtKa2hv32J196qr1dtp8cYaNot2BhFKumLlTu56cWvaNsolVduGRJY54SISHWipD9gsZD0T1u6jXtfW0CCGX+//BSGd69+ZRjX7drPn99fxruLttCkXi3uObcLlw9oS1KiVnolHIZNc0oT/d1rAIP2Q70kv/sF0LBd0FGKVInPVuzg5hfnkNGkLi/fPJgmKvUrIgIo6Q9cdU76i0Nh/jJ1Gf/+ZDW9W6fx5NX9qn2Zu/nrd/Pw5Ey+Wrubzs3q8eD53RnevVnEJxlXO6EiWPeFn+hPgn1bISEZOp7pJfrdRkG9ZkFHKVKlpi/bzq3/nUunpvUYe/Ng0utqsrmISAkl/QGrrkn/9tx87nxlPrPWZHP14Hb8YnTPmKmP75xj6tJtPDIlizU79zOkYzoPjepJ7zZpQYcWWUV5sOpjb4z+ssmQtxuSU6HzOdDjQug6AmrH+e9AaqyPs7bz/f/OpUvzerx802AaKeEXETmEkv6AVcekf+bqXdw5bj65+UU8fHFvLul34qvrBqkoFGbc7PU89sEKsvcXclGfVtw3olu1v1txXPL3woqpXo/+imlQtN9L7Lue7/XodxoOKXF0viJH8MHSbfxw7Dy6tajPf28aRMNUJfwiIodT0h+w6pT0O+f496er+cv7y2ifnsr/XdM/Lkph5uYX8dQnq3j2szU44IahHfjhsM6k1an6hcSiYv9Oryc/c6K3Om6oEOo2gx7+RNwO34LEGD03keM0dclWbn9lHj1bNuClmwbH7vtaRCTClPQHrLok/Tl5Rdz3+kKmLd3GqN4t+NOlJ1M/AqvrBmnznjwenbqct+ZvJK1OMncO78K1Q9qTkhQDk31zNvo19Cd6Y/Vd2Jt82+NCL9FvM1A19KXGeW/xFu54ZT6926Tx4o2DIrIiuIhIvFDSH7DqkPQv2ZzDD8fOY9PuPH42qgc3nNYhrie+Ltmcwx8nZ/H5yp20S0/lgZHdGdW7RfU7550rvYWyMifC5nleW9MepTX0W/RWDX2psd5dtIW7xs+nT9uGvHDDwLjrpBARqWpK+gMWdNL/6lfr+cX/lpCemsK/ru5H//aNAoslmpxzfLJ8B49MySJray592zXkoVE9GBDF1YWPEBRs/bq0tOaOTK+9dX+/tOYYaNI5uPhEqokJCzdzz6sL6NeuIc/fMIh6WpdDROSYlPQHLKikP68wxC//t5jX527k9M5NePyKPjSugfWsQ2HHm3M38ui0ZWzbW8B5vZrzwMjudGxaLzoBhMOwcXZpor9nHVgCtD+ttIZ+WmxOpBaJhHfmb+Le1xYwsEM6/7l+oBbiExGpICX9AQsi6V+7cz8/eHkuWVtzuWt4Z+4+p3qsrhukA4XFPPfZGp76ZBUFxWGuHtyOu87uEpkLoVARrP3MS/Kz3oV92yAxBToO82vonw91m1T9zxWJcW/O3cj9byxkcEZjnrt+AKkpSvhFRCpKSX/Aop30v7d4K/e/vpDEROPvl/dhWDct0FTWjtwCHvtgOeO/2kCd5ERuO6sTN52eUfk1CgoPwKqPvER/+RTIz4HkutDlXC/R7zICajeompMQiUOvzdnAA28u4rROTXjmewOok6KJ6yIix0NJf8CilfQXhcL85f1lPP3pak5pk8a/ru5Hm0aq3340K7fv45EpWXyQuY2WabX58YhuXNK3NQnHc0ckPweWT/Um4678AIoOQO2G3pCd7qOh0zBIrhO5kxCJE+Nnr+enb33Nt7p4CX+sLBQoIlKdKOkPWDSS/m17vdV1Z6/N5toh7fn56B7UStKHZkXMXL2LP07OZOHGHHq2bMDPRvXg9C7lDL3Zv7O0tObq6RAugnotSmvotz9NNfRFjsPYWet46O3FnNWtKU9d018Jv4jICVLSH7BIJ/0zVnmr6+4vKOaRS3tzUZ/WEftZ8SocdkxctJm/vL+MjbvzOLNrUx4c1Z3uLfzhODmbIGvSYTX020PPC706+q0HQEIMrAUgUs28NGMtv/zfEs7u3ownr+mnzgoRkUpQ0h+wSCX94bDjqU9X8df3l5HRpC5PXdOfLs1jf3XdIBUUh3jpy3X886MVNC7YyP3tlnOuzSJ563xvh5Ia+j0vhOYnqYa+SCU8/8UafjNxKef2bM4TV/VVwi8iUklVkfSrfEI1k3OgiB+/voAPMrcz+uSWPHLpyapjXVnOUWtnJreEJnJj0wkk7lgK2+Br15E97W+n38hrqduqR9BRisSFZz9bze/fzeS8Xs3555X9YmPVbBGRGkDZZDWyeFMOt42dy9acfH5zYS++d2r76rfSbKwIh72VcEtWxc1eDRiJ7YfCyEfY1OJs/v3lPiYt2kKTzZu459xULh/QlqREJSgiJ+rpT1fx8OQsRvVuweNX9CVZ7ycRkWpDw3sqoaqG9zjnGDd7A7+euIQmdVN44up+9GtXM1bXrVKhYlg/w0/0J0HuZkhIgowzSxfLqndomdP563fzx8lZzF6bTedm9fjpyO6c3aOZLrZEjtOT01fy5/eWMeaUVvz9u6foAlpEpAppTH/AqiLpzysM8dA7X/PWvE18q0sTHr+iL+l1U6oowhqguABWf+Il+ssmw4FdkFQbOp/jTcTtOgLqlH8B5Zxj2tJtPDIli9U79zM4I52HLujByW0aRukkRGLbEx+t4K9Tl3NRn1Y8+h0l/CIiVU1Jf8Aqm/Sv3rGPH46dx7Jtudw1vAt3nd2lxq+uWyGF+73a+ZkTYfn7ULAXajWArud5Pfqdz4GUusd92KJQmPGz1/PYByvYtb+QC09pxV1nd6FJvRQSE+zgv6SEBBIM3Q0QAR77YDmPfbCCS/q25i/fOUV/w0REIkBJf8Aqk/RP+XoL97+xiORE47Er+nJm16ZVHF2cydvjJfgli2UV50NqY+g2CnpeBBlnQFKtKvlRuflF/PuT1Tzz2WoKisNH3e/ghYAZSQlGYqL3NaHM94lW5kIhwW8/5ALiyI8TExLKOVbp90n+vokJlD6nQj/nsOeYkZTobU9JTKB2ciKpKd6/2smJ1EpK0EWOHMI5x9+nLecfH63ksv5t+NOlJyvhFxGJEFXviUFFoTCPTMniuc/X0KdtQ/51dT9aN9TKrke0b3vpYllrPoFwMdRvBf2u83r0250KiVX/X7h+7WTuO68bVw9px4eZ2ykKhQmFHaGwo7jM1/DB78OEwhAKh7125ygOldnfOUIhV7rt4HMcRaEweUVlj3X4scv+3CPHEQ0JBqkpSdTxLwTqJCeWeey3l2kruVhITUny9vnG80rb6yQnasJnjHHO8depy/jXx6u4YmBbHr649/GteC0iIlGnpD+Ktubkc8cr85izbjfXD+3Az0b1UDm7w+3ZUGaxrC8BB40y4NTbvTH6rfpFbbGslml1uGZI+6j8rMoouUA4eEER8i40iv2LhOJQ2YuNwy8kSh6HCYehOBymsDhMXlGIvMIQBwpDhz0u5oD/OL/I+5q9P4+8wuJD9j3ei5HkRKNOmYuEkjsNh14sJB28oCi5WPAeJ5HqP65dctGRfOgFihLSquOc45H3svj3J6u5anA7fn/RDwiu1QAAFmtJREFUSfr9iojEACX9UfLFyp3cPX4+BwpD/OPKvlx4SqugQ6o+dq4oLa252V8sq1kvOPMBr0e/eS8tllWOhAQjpZolXYXFYe9Coaj4kIuHA4XeRUHJxcM3LyyKy+wTIje/mO17Cw4exztmiOMdlVgrKcG/YEg6eMFQ9q5EiwZ1GJSRzsAOjWhcr2qGicUj5xwPT87kmc/WcO2Q9vzmwl5K+EVEYoSS/ggLhx1PTl/J36Ytp2PTeoy/tR+dm9Xw1XWdg61fe0l+5kTYkem1t+4P5/zGS/Qbdwo2RqmUlKQEUpISSCO5yo/tnKOgOFzmYqH07kPeIRcX37wrceCwC47s/YVs3B3iw8zt/OeLNQB0aVaPQRnpDMpIZ3BGY1qk1a7yc4hFzjl+O2kpz3+xluuHduBXY3pqnoeISAxR0h9Bew4Ucs+rC/h42Q4u6tOKhy/uTd2aurpuOAyb5pT26O9eC5YA7U+DAX/2auintQk6SokBZkbtZG8IUFUpKA6xeFMOs9ZkM3tNNv9bsJmxs9YD0C49tcxFQDrt0lNrXLLrnOPXE5bw4ox13HhaBr8Y3aPG/Q5ERGKdqvdUQnnVexZt3MNtL89je24+vxzdk2uG1MDVdUPFsO6L0sWy9m2FhGToeJbXm99tFNRT1SKpfopDYbK25jJz9S5mr8nmq7XZ7D5QBECLBrUPuQjo3KxeXL+3w2HHLycs5uWZ67n1jI48eH73uD5fEZHqSCU7A3akpN85x9hZ6/ntxKU0rV+Lf13djz5ta9AiT0X5sHq615u/7F3I2w1JdaBLyWJZ50HttKCjFDku4bBj5Y59B+8EzFq9i+25BQCk101hYIdGDMpozOCMdHq0bBA3pSvDYcdD7yxm3Oz1/ODMTjwwspsSfhGRAKhkZzVzoLCYh95ezNvzN3Fm16Y8dnkfGtWE1XUL9sHKabB0AqyYCoX7oFYadBvp9eh3OhtSUoOOUuSEJSQYXZvXp2vz+lw7pD3OOdZnHzh4ETB7TTbvL9kGQP1aSfTv0OjgnYDerRvGZJWucNjx4Ftf8+qcDdwxrDM/HtFVCb+ISAxT0l9FVu3Yx20vz2XF9n3ce25X7hjWOb6rWhzIhuXveT36Kz+EUAGkNoGTLvV69DPOgKQacMEjNZKZ0b5xXdo3rst3B7QFYEtOnncXwL8ImL5sGQC1kxPo167RwSFBfds2ok5K1c1HiIRQ2PHAm4t4Y+5G7j67Cz86p4sSfhGRGKfhPZVQMrxn0qLNPPDGImolJ/KPK/pyepcmQYcWGbnbSmvor/3MWyyrQRuvN7/HGGg3BBKqdzIjEi079xUwZ23pRcDSLXtxzluT4OQ2DQ9eBPRv34gGtau+ytGJCoUd972+kLfnb+Kec7py9zldgg5JRKTGq9Zj+s2sLfAS0AIIA0875x4/bJ8zgMeAk4ErnHNvlNn2HjAE+Nw5N7pMewYwHkgH5gHXOucKDzuuAY8Do4ADwPXOuXn+tuuAn/u7/t4596Lf3h94AagDTAbudsf45fTvP8CN+dWLvPDlWvq181bXbZkWZ6vr7llfWlpz/UzAQXon6Hmhl+i36qca+iIVkJNXxLx1u/2LgF0s2phDcdiRYNCzVQMGdWh88EIgPaBhgcWhMPe+tpAJCzdz/3nduH1Y50DiEBGRQ1X3pL8l0NI5N8/M6gNzgW8755aW2acD0AC4D5hwWNJ/NpAKfP+wpP814C3n3HgzewpY6Jz7v8N+9ijgTrykfzDwuHNusJmlA3OAAYDzY+rvnNttZrOBu4GZeEn/P5xzU8o7x0btu7u0Kx/lhtM68OD5cbS67s6VkPk/b4z+lgVeW/OT/B79C6FZDyX6IpV0oLCYBev3HLwTMG/9bgqKwwB0bV6yVkBjBnVIj8paAUWhMD96dQHvLtrCAyO7c9tZWitDRKS6qNYTeZ1zW4At/uNcM8sEWgNLy+yzFsDMwkd4/odmdlbZNr8Hfzhwld/0IvBr4JCkH7gIeMnvqZ9pZg39i5CzgGnOuWz/eNOAkWY2HWjgnJvht78EfBsoN+nPLwrz8lX9uODkluXtVv05B9uWeKU1l07QYlkiUZCaksTQzk0Y2tkbDlhQHOLrjaVrBbwzfzMvz/TWCmjfOJVBHUoXDGubXqdKx9gXhcLcNW4+UxZv5aFRPbjljI5VdmwREakeojKR1+/R7wvMquShGgN7nHPF/vcb8S4kDtca2FDm+5L9ymvfeIT2cnVuVi92E37nYNM8r0c/cyJkrwYM2g+FkX+CHqO1WJZIFNVKSmRAh3QGdEjn9mHeUJvMLbnMWuOtFTAtcxuvz/X+TFXlWgGFxWHuHDeP95ds4xeje3LT6RlVeVoiIlJNRDzpN7N6wJvAj5xzeyt7uCO0HWl80tH2O972bx7Y7FbgVoB27dodOcrqKhzyxuWXrIq7dxMkJHmVdobe5a2KW69Z0FGKCJCUmEDvNmn0bpPGzd/q+I21Amau3sWEhZsBb62AkjsBg45jrYCC4hC3j53PB5nb+PWYnlx/mhJ+EZF4FdGk38yS8RL+sc65t6rgkDuBhmaW5Pf2twE2H2G/jUDbMt+X7LcRb4hP2fbpfnubI+z/Dc65p4GnwavecyInEVWhIljziZfkZ70L+3dAYi3ofDYM/4VXS79Oo6CjFJFjKG+tgFmrs5m9dhfvLdkKeGsFDPAXDBuUkU7v1mnfmHOUXxTih2Pn8VHWdn53US+uPbVDAGclIiLRErGk3x9//xyQ6Zz7W5n2OwCcc08c7zGdc87MPgYuw6vgcx3wP/+4FwODnHMPAhOAO8xsPN5E3hzn3BYzex942MxKstwRwIPOuWwzyzWzIXhDkL4H/POETrw6KMqDVR/5q+JOhvwcSK4LXUd4E3G7jIBa9YKOUkQq4UhrBWzek8dXZcqEfrwsC/jmWgG9WqZx1/j5fLJ8Bw9f3JurBsfYXUsRETlukazeczrwGfA1XslOgJ/hVdT5wjk3zswGAm8DjYB8YKtzrpf//M+A7kA9YBdwk3PufTPrSGnJzvnANc65AjO7D0h2zv3Rv+B4AhiJV7LzBufcHP+4N/pxAPzBOfe83z6A0pKdU4A7j1Wys6ROf7VQkOuthps5EZZPhaL9UDsNuo3yEv1OwyA5zsqJiki5jrZWAHgFuB65pDeXD1TCLyJS3VXrkp1H/YFmk4BLDq+tXwXHfRm4xzm3oyqPW57Ak/683bBsyqGr4tZt6o3NL1kVN7H6LPojIsEqWStgzrps+rZtxDk9mwcdkoiIVEBMJv3xJJCkf9/20lVx13yqVXFFRERE4ly1rtMvVShno5fkL50A62fgrYrbEU69w+vRb61VcUVERETk6JT0V1e7VpUulrV5ntfWrCec+YDXo9+8lxJ9EREREakQJf3VhXOwPbM00d++xGtv1RfO/pXXo9+kc7AxioiIiEhMUtIfJOdg8/zSRD97FWDeuPzz/uitittQlTVEREREpHKU9EdbOAQbZnlj9DMnQs4GsETI+BacertXead+i6CjFBEREZE4oqQ/GkJFsPZzr0c/cxLs3w6JKdBpOJz1IHQ7H1LTg45SREREROKUkv5IKcqH1dO9RH/ZZK+mfnIqdDm3dFXc2g2CjlJEREREagAl/VWpYB+s/MBL9JdPhcJcqJUG3Ub6q+IOh5TUoKMUERERkRpGSX9l5e2B5e/5q+J+AMX5kNoYTroYelzkrYqblBJ0lCIiIiJSgynpr4zsVfCXzhAugvotod/3vB79dqdCon61IiIiIlI9KDOtjKICGHKv16Pfuj8kJAQdkYiIiIjINyjpr4zmPWHE74OOQkRERESkXOqaFhERERGJc0r6RURERETinJJ+EREREZE4p6RfRERERCTOKekXEREREYlzSvpFREREROKckn4RERERkTinpF9EREREJM4p6RcRERERiXNK+kVERERE4pySfhERERGROKekX0REREQkzinpFxERERGJc+acCzqGmGVmecCSoOOIojQgJ+ggokznXDPonGsGnXPNUNPOuaadL9TMc+7inEurzAGSqiqSGmqfc25A0EFEi5k97Zy7Neg4oknnXDPonGsGnXPNUNPOuaadL9Tcc67sMTS8p3L2BB1AlE0MOoAA6JxrBp1zzaBzrhlq2jnXtPMFnfMJ0fCeSjCzOTWpp19EREREYpN6+iun0rdaREREREQiTT39IiIiIiJxTj39cpCZhcxsQZl/HcrZ9ywzmxS96CLDzJyZ/bfM90lmtiMezu1YzOxi//y7Bx1LJNXk1xjAzPYFHUMQjnXeZjbdzGJ+eGZNeR+XZWYPmdkSM1vkf1YNDjqmSDOzNmb2PzNbYWarzOxxM0spZ/8fmVlqNGOsSv7/6UfLfH+fmf06wJAiqkz+tcTMFprZvWZW5Tm6kv5jqGEfmHnOuT5l/q0NOqAo2A+cZGZ1/O/PBTYdzwHMLFarYF0JfA5ccTxPMrPEyIQTMZV+jUWqsRN6H8cqMzsVGA30c86dDJwDbAg2qsgyMwPeAt5xznUBugL1gD+U87QfATGb9AMFwCVm1iToQKKkJP/qhfcZNQr4VVX/ECX9Ui4zSzSzv5jZV36vyvfLbG5gZm+b2VIzeyoSV6VRMgW4wH98JTCuZIOZDTKzL81svv+1m99+vZm9bmYTganRD7lyzKwecBpwE36y4N+9+fRIr6mZ7TOz35rZLODU4CI/YSfyGn9mZn3K7PeFmZ0c1airyOF35szsCTO73n+81sx+Y2bzzOzreOoxLu+840E57+OjvdajzCzLzD43s3/E6N2ulsBO51wBgHNup3Nus5n1N7NPzGyumb1vZi3h4B2dx/z39mIzGxRo9CdmOJDvnHsewDkXAu4BbjSzumb2V/+9u8jM7jSzu4BWwMdm9nGAcVdGMd68yXsO32Bm7c3sQ/98PzSzdmaW5v8tK/nMSjWzDWaWHO3AK8s5tx24FbjDPEfNw8zsJ/5rv9DMHjnWsWM1SYsqM6vn/8cq+VC8yG/vYGaZZvaMf0tmapnexFhUx0qH9rztt90E5DjnBgIDgVvMLMPfNgj4MdAb6ARcEvWIq8Z44Aozqw2cDMwqsy0LOMM51xf4JfBwmW2nAtc554ZHLdKq823gPefcciDbzPr57Ud7TesCi51zg51zn0c92so7kdf4WeB6ADPrCtRyzi2KWsTRtdM51w/4P+C+oIORCjva+/gb/P/7/wbOd86dDjSNUoxVbSrQ1syWm9mTZnamn9j9E7jMOdcf+A+H9oLXdc4NBX7ob4s1vYC5ZRucc3uB9cDNQAbQ17/zMdY59w9gMzDMOTcs2sFWoX8BV5vZ4QtSPQG8VHK+wD+ccznAQuBMf58xwPvOuaKoRVuFnHOr8XL0ZhwlDzOz8/H+Bgx2zp0C/PlYx1XSXzH5wMX+h+Iw4FEzM39bF+Bf/i2ZPcClAcVYFcoO77nYbxsBfM/MFuAlSo3xzhlgtnNutd/rMA44PfohV56fyHXA6wGefNjmNOB1M1sM/B3vj2+Jac657KgEWfWuxEuE8b9e6T8+2msaAt6MbohV5wRf49eB0X5CcSPwQlSCDcZb/te5eL8niQ1Hex8fSXdgtXNujf/9uHL2rbacc/uA/ng9oTuAV4HvAycB0/zPqp8Dbco8bZz/3E/x7lA3jGrQlWfAkaquGHAG8JRzrhgghj+TvsG/sHkJuOuwTacCr/iP/0vp59SrwOX+4yv872NZSZ55tDzsHOB559wBqNhrH6tjkaPNgIfN7AwgDLQGmvvb1jjnFviP4/ED04A7nXPvH9Jodhbf/CMUy6WgJgB/Bc7Ce0OV+B3wsXPuYvMmNk8vs21/lGKrUmbWGO928Ulm5oBEvNduMkd/TfP9C4FYdlyvsXPugJlNAy4CvgvE8qTPYg7t5Kl92PYC/2uI+PpcONZ5x6xy3scTOPI5G3HC/1s0HZhuZl8DtwNLnHNHG3oY659VSzisQ9HMGgBtgdXE3vkcj8eAecDz5exTcv4TgD+aWTreheFHEY4tYsysI97f4+0cPQ8byXG+9urpr5ir8W6F9nfO9QG2UfqHtKDMfvH2gQnwPnBbybg4M+tqZnX9bYP8W0wJeFfXsTjso8R/gN86574+rD2N0kmf10c1osi5DO/WaHvnXAfnXFtgDV5vSTy9poc7kdf4WeAfwFcx3oO2DuhpZrX8W+VnBx1QlMTzeR/tfQxHPucsoKOVVmW7nBhkZt3MrEuZpj5AJtDUvEm+mFmymZW9K3u533463jCJnKgFXDU+BFLN7HtwsJjCo3h3H6cCPzC/oISf8ALkAvWjH2rV8v/uvoY3xKXEl5ROXL8a/3PKvws0G3gcmBSrHVVm1hR4CnjCeXX1j5aHTcWb15Hqt6cf7ZgllPRXTBqw3TlXZGbDgPZBBxRFzwJLgXn+8Id/U3phMwN4BFiM92Hz9hGPEAOccxudc48fYdOf8XoOvsDrSYsHV/LN1+pN4Cri6DU93Im8xs65ucBeyu9lqrb8RKDAObcB74NzEd4Y2PmBBhZhNeS8y3sff+OcnXN5eGPa3zOzz/E6r2It+QWvas2L5hUbWAT0xJuLcxnwJzNbCCwAhpZ5zm4z+xIvkbrp8ANWd37idzHwHTNbASzHG3b8M7zP6PXAIv/cr/Kf9jQwJYYn8pb1KFC2is9dwA3+638tcHeZba8C1xB7Q3tK5lQuAT7AS+h/4287Yh7mnHsP7+7GHH/ozzHnY2lxrnL4HxzbgG7ARCAZ74/JacD5/m6TnHMn+fvfB9Rzzv06+tGKVI4/ZOs+59zooGOpLsysFd4wgu7OuXDA4Rw3MzsFeMY5F4sVS05YTT3vYzGzes65ff6ctH8BK5xzfw86rkgys+l4f9fmBB2LSNDibShKVesFrHLO7eToZQpPKnngnPtrVKISkYjzb6X/Abg3RhP+H+D1iP0o6FiiqaaedwXdYmbXASl4dwD+HXA8IhJF6uk/irIfHM65mKvDLiIiIiJSQkm/iIiIiEic00ReEREREZE4p6S/DDNra2Yf+6vsLjGzu/32dDObZmYr/K+N/PbuZjbDzAr8Sbxlj3WPf4zFZjbOXw1RRERERCTqlPQfqhj4sXOuBzAEuN3MegI/BT50znXBq5f7U3//bLxx/4dM4DWz1n77AL+yTyKlNWVFRERERKJKSX8Zzrktzrl5/uNcvAU/WuOtyPmiv9uLwLf9fbY7574Cio5wuCS8uqtJQCqwOcLhi4iIiIgckZL+o/BXLewLzAKaO+e2gHdhADQr77nOuU14vf/rgS14KwCqApCIiIiIBEJJ/xGYWT28lQ1/5JzbewLPb4R3dyADaAXUNbNrqjZKEREREZGKUdJ/GDNLxkv4xzrn3vKbt5lZS397S2D7MQ5zDrDGObfDOVcEvMWhS4KLiIiIiESNkv4y/KXJnwMynXN/K7NpAnCd//g64H/HONR6YIiZpfrHPBtvfoCIiIiISNRpca4yzOx04DPgayDsN/8Mb1z/a0A7vIT+O865bDNrAcwBGvj77wN6Ouf2mtlvgMvxKgLNB252zhVE83xEREREREBJv4iIiIhI3NPwHhERERGROKekX0REREQkzinpFxERERGJc0r6RURERETinJJ+EREREZE4p6RfRERERCTOKekXEREREYlzSvpFREREROLc/wPtNjmuQ9f4oQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jLpTQbVPZ7Pl",
        "colab_type": "text"
      },
      "source": [
        "### Evaluate the Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q3OBfB_RZ7Pm",
        "colab_type": "code",
        "outputId": "86fe5073-ed68-4568-bf2f-eebee3272987",
        "colab": {}
      },
      "source": [
        "from sklearn.metrics import mean_squared_error\n",
        "\n",
        "error = mean_squared_error(test['Inventories'], predictions)\n",
        "print(f'ARIMA(1,1,1) MSE Error: {error:11.10}')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ARIMA(1,1,1) MSE Error: 60677824.72\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GPBYNCVcZ7Pp",
        "colab_type": "code",
        "outputId": "b3465f15-43a1-48c4-fd31-4ebde02f1574",
        "colab": {}
      },
      "source": [
        "from statsmodels.tools.eval_measures import rmse\n",
        "\n",
        "error = rmse(test['Inventories'], predictions)\n",
        "print(f'ARIMA(1,1,1) RMSE Error: {error:11.10}')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ARIMA(1,1,1) RMSE Error: 7789.597212\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EYQqP2Z-Z7Ps",
        "colab_type": "text"
      },
      "source": [
        "### Forecast into the future"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AIIQwSZaZ7Pt",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "model = ARIMA(df2['Inventories'],order=(1,1,1))\n",
        "results = model.fit()\n",
        "fcast = results.predict(len(df2),len(df2)+11,typ='levels').rename('ARIMA(1,1,1) Forecast')"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J6BggU__Z7Pw",
        "colab_type": "code",
        "outputId": "62669680-ce79-42e9-a0fa-92c2435d6738",
        "colab": {}
      },
      "source": [
        "# Plot predictions against known values\n",
        "title = 'Real Manufacturing and Trade Inventories'\n",
        "ylabel='Chained 2012 Dollars'\n",
        "xlabel='' # we don't really need a label here\n",
        "\n",
        "ax = df2['Inventories'].plot(legend=True,figsize=(12,6),title=title)\n",
        "fcast.plot(legend=True)\n",
        "ax.autoscale(axis='x',tight=True)\n",
        "ax.set(xlabel=xlabel, ylabel=ylabel)\n",
        "ax.yaxis.set_major_formatter(formatter);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}