11. ARIMA and Rolling Forecast.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ARIMA and Rolling Forecast\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from datetime import datetime\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 데이터 읽기와 포매팅\n",
    "\n",
    "데이터는 3년치 월별 샴푸 판매량으로 [Data Market](https://datamarket.com/data/set/22r0/sales-of-shampoo-over-a-three-year-period#!ds=22r0&display=line) 에서 다운로드 받아 저장한 CSV 파일을 사용합니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Month 칼럼을 읽기 위한 파서\n",
    "def dateparser(x):\n",
    "    return datetime.strptime('190'+x, \"%Y-%m\")\n",
    "#    \"1-01\" => \"1901-01\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "shampoo = pd.read_csv('data/sales-of-shampoo.csv', index_col='Month', parse_dates=True, date_parser=dateparser)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "DatetimeIndex: 36 entries, 1901-01-01 to 1903-12-01\n",
      "Data columns (total 1 columns):\n",
      "Sales of shampoo    36 non-null float64\n",
      "dtypes: float64(1)\n",
      "memory usage: 576.0 bytes\n"
     ]
    }
   ],
   "source": [
    "shampoo.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Sales of shampoo</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1901-01-01</th>\n",
       "      <td>266.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1901-02-01</th>\n",
       "      <td>145.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1901-03-01</th>\n",
       "      <td>183.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1901-04-01</th>\n",
       "      <td>119.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1901-05-01</th>\n",
       "      <td>180.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Sales of shampoo\n",
       "Month                       \n",
       "1901-01-01             266.0\n",
       "1901-02-01             145.9\n",
       "1901-03-01             183.1\n",
       "1901-04-01             119.3\n",
       "1901-05-01             180.3"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shampoo.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize the data\n",
    "\n",
    "pandas 내장 플로팅 함수들로 시계열 데이터를 시각화 해봅니다. 뚜렷한 트랜드를 보이는 반면 시즌 패턴은 보이지 않습니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f285e1c94e0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "shampoo.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing for Stationarity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.tsa.stattools import adfuller"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def adf_check(ts):\n",
    "    result = adfuller(ts)\n",
    "    if result[1] <= 0.05:\n",
    "        print('Stationary {}'.format(result[1]))\n",
    "    else:\n",
    "        print('Non-Stationary {}'.format(result[1]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Non-Stationary 1.0\n"
     ]
    }
   ],
   "source": [
    "adf_check(shampoo['Sales of shampoo'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "테스트 결과 데이터가 stationary 특성을 보이지 않고 있음이 확인됩니다.\n",
    "\n",
    "## Differencing\n",
    "\n",
    "시계열 데이터에 대한 1차(first) difference 는 다음 스탭으로의 한 차원(시간단위) 만큼의 변화값의 series 입니다. pandas 를 이용하면 아주 differencing 할 수 있습니다. 1차, 2차 등 differencing 을 시도해보고 stationary 한 차원을 찾습니다."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### First Difference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "shampoo['1st diff'] = shampoo['Sales of shampoo'] - shampoo['Sales of shampoo'].shift(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stationary 1.7998574141687034e-10\n"
     ]
    }
   ],
   "source": [
    "adf_check(shampoo['1st diff'].dropna())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f285de98e80>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "shampoo['1st diff'].plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Second Difference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "shampoo['2nd diff'] = shampoo['1st diff'] - shampoo['1st diff'].shift()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stationary 0.0039063349396599245\n"
     ]
    }
   ],
   "source": [
    "adf_check(shampoo['2nd diff'].dropna())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f285b4f4d30>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "shampoo['2nd diff'].plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Autocorrelation and Partial Autocorrelation Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "from statsmodels.graphics.tsaplots import plot_acf,plot_pacf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "ax1 = fig.add_subplot(211)\n",
    "fig = plot_acf(shampoo['2nd diff'].dropna(), ax=ax1)\n",
    "ax2 = fig.add_subplot(212)\n",
    "fig = plot_pacf(shampoo['2nd diff'].dropna(), ax=ax2, method='ywm')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12,8))\n",
    "ax1 = fig.add_subplot(211)\n",
    "fig = plot_acf(shampoo['1st diff'].dropna(), ax=ax1)\n",
    "ax2 = fig.add_subplot(212)\n",
    "fig = plot_pacf(shampoo['1st diff'].dropna(), ax=ax2, method='ywm')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PACF 와 ACF 에서 각각 lag 1 에 대해 강한 상관관계를 보이고 있습니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.tsa.arima_model import ARIMA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = ARIMA(shampoo['Sales of shampoo'], order=(1,1,1), freq='MS')\n",
    "model_fit = model.fit(disp=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                             ARIMA Model Results                              \n",
      "==============================================================================\n",
      "Dep. Variable:     D.Sales of shampoo   No. Observations:                   35\n",
      "Model:                 ARIMA(1, 1, 1)   Log Likelihood                -197.233\n",
      "Method:                       css-mle   S.D. of innovations             66.625\n",
      "Date:                Thu, 31 Jan 2019   AIC                            402.467\n",
      "Time:                        19:34:34   BIC                            408.688\n",
      "Sample:                    02-01-1901   HQIC                           404.614\n",
      "                         - 12-01-1903                                         \n",
      "============================================================================================\n",
      "                               coef    std err          z      P>|z|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------------\n",
      "const                       12.0965      3.651      3.313      0.002       4.940      19.253\n",
      "ar.L1.D.Sales of shampoo    -0.5674      0.161     -3.526      0.001      -0.883      -0.252\n",
      "ma.L1.D.Sales of shampoo    -0.5133      0.155     -3.303      0.002      -0.818      -0.209\n",
      "                                    Roots                                    \n",
      "=============================================================================\n",
      "                  Real          Imaginary           Modulus         Frequency\n",
      "-----------------------------------------------------------------------------\n",
      "AR.1           -1.7625           +0.0000j            1.7625            0.5000\n",
      "MA.1            1.9483           +0.0000j            1.9483            0.0000\n",
      "-----------------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "print(model_fit.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "일단 residual error 에 대해 line plot 을 그려고보 모델에 의해 파악되지 않은 트랜드 정보가 있는지 확인합니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2858557e10>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot residual errors\n",
    "model_fit.resid.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "다음으로 residual error 에 대한 density plot 을 그리고 정규분포에 가까운지 확인합니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f28584ebd30>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_fit.resid.plot(kind='kde')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count     35.000000\n",
       "mean      -5.505160\n",
       "std       69.978598\n",
       "min     -132.196527\n",
       "25%      -42.395612\n",
       "50%       -4.181400\n",
       "75%       21.540075\n",
       "max      142.155114\n",
       "dtype: float64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_fit.resid.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GridSearch\n",
    "AIC 를 기준으로 최적의 p,d,q 파라메터를 찾습니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "import itertools\n",
    "\n",
    "p = range(0,5)\n",
    "d = range(1,3)\n",
    "q = range(0,5)\n",
    "\n",
    "pdq = list(itertools.product(p, d, q))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/scipy/signal/signaltools.py:1341: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  out_full[ind] += zi\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/scipy/signal/signaltools.py:1344: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  out = out_full[ind]\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/scipy/signal/signaltools.py:1350: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  zf = out_full[ind]\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(0, 1, 0) - AIC:430.87311187552797\n",
      "ARIMA(0, 1, 1) - AIC:409.0126622411526\n",
      "ARIMA(0, 2, 0) - AIC:461.1578257086931\n",
      "ARIMA(0, 2, 1) - AIC:424.58251674821\n",
      "ARIMA(1, 1, 0) - AIC:406.02228959235015\n",
      "ARIMA(1, 1, 1) - AIC:402.4666524179953\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(1, 1, 2) - AIC:401.5247943798928\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(1, 1, 3) - AIC:403.52417287508956\n",
      "ARIMA(1, 2, 0) - AIC:423.90008603782104\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/tsatools.py:676: RuntimeWarning: invalid value encountered in log\n",
      "  invmacoefs = -np.log((1-macoefs)/(1+macoefs))\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tools/numdiff.py:96: RuntimeWarning: invalid value encountered in maximum\n",
      "  h = EPS**(1. / s) * np.maximum(np.abs(x), 0.1)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/base/model.py:488: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n",
      "  'available', HessianInversionWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(1, 2, 3) - AIC:nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/tsatools.py:676: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  invmacoefs = -np.log((1-macoefs)/(1+macoefs))\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/tsatools.py:650: RuntimeWarning: invalid value encountered in true_divide\n",
      "  newparams = ((1-np.exp(-params))/(1+np.exp(-params))).copy()\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/tsatools.py:651: RuntimeWarning: invalid value encountered in true_divide\n",
      "  tmp = ((1-np.exp(-params))/(1+np.exp(-params))).copy()\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tools/numdiff.py:243: RuntimeWarning: invalid value encountered in add\n",
      "  **kwargs)).imag/2./hess[i, j]\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tools/numdiff.py:243: RuntimeWarning: invalid value encountered in multiply\n",
      "  **kwargs)).imag/2./hess[i, j]\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/tsatools.py:650: RuntimeWarning: invalid value encountered in exp\n",
      "  newparams = ((1-np.exp(-params))/(1+np.exp(-params))).copy()\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/tsatools.py:651: RuntimeWarning: invalid value encountered in exp\n",
      "  tmp = ((1-np.exp(-params))/(1+np.exp(-params))).copy()\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/base/model.py:488: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n",
      "  'available', HessianInversionWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(1, 2, 4) - AIC:nan\n",
      "ARIMA(2, 1, 0) - AIC:403.6275641166603\n",
      "ARIMA(2, 1, 1) - AIC:404.28621423318384\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(2, 2, 0) - AIC:412.99938249704275\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(2, 2, 1) - AIC:396.65262382813955\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(2, 2, 3) - AIC:389.68350650892074\n",
      "ARIMA(3, 1, 0) - AIC:404.6924591816878\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(3, 1, 1) - AIC:406.1395443929549\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/tsatools.py:607: RuntimeWarning: invalid value encountered in true_divide\n",
      "  (1+np.exp(-params))).copy()\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/tsatools.py:609: RuntimeWarning: invalid value encountered in true_divide\n",
      "  (1+np.exp(-params))).copy()\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(3, 2, 0) - AIC:410.9109265845758\n",
      "ARIMA(3, 2, 1) - AIC:396.30623658353767\n",
      "ARIMA(3, 2, 2) - AIC:nan\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/base/model.py:488: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n",
      "  'available', HessianInversionWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/base/model.py:488: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n",
      "  'available', HessianInversionWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(3, 2, 3) - AIC:406.104929451703\n",
      "ARIMA(4, 1, 0) - AIC:404.78676855669903\n",
      "ARIMA(4, 1, 1) - AIC:406.5796403612012\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(4, 1, 2) - AIC:400.2307795387626\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(4, 1, 3) - AIC:400.65677258685764\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(4, 1, 4) - AIC:406.3808484357497\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(4, 2, 0) - AIC:403.9482289506873\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(4, 2, 1) - AIC:393.1540750944809\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/base/model.py:488: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n",
      "  'available', HessianInversionWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ARIMA(4, 2, 2) - AIC:nan\n",
      "ARIMA(4, 2, 3) - AIC:402.5718428919337\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/base/model.py:488: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n",
      "  'available', HessianInversionWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    }
   ],
   "source": [
    "aic_params = []\n",
    "\n",
    "for param in pdq:\n",
    "    try:\n",
    "        mod = ARIMA(shampoo['Sales of shampoo'], order=param)\n",
    "        results = mod.fit(disp=0)\n",
    "        print('ARIMA{} - AIC:{}'.format(param, results.aic))\n",
    "        aic_params.append((results.aic, param,))\n",
    "    except:\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n",
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.\n",
      "  % freq, ValueWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                              ARIMA Model Results                              \n",
      "===============================================================================\n",
      "Dep. Variable:     D2.Sales of shampoo   No. Observations:                   34\n",
      "Model:                  ARIMA(4, 2, 1)   Log Likelihood                -189.577\n",
      "Method:                        css-mle   S.D. of innovations             56.216\n",
      "Date:                 Thu, 31 Jan 2019   AIC                            393.154\n",
      "Time:                         19:34:44   BIC                            403.839\n",
      "Sample:                     03-01-1901   HQIC                           396.798\n",
      "                          - 12-01-1903                                         \n",
      "=============================================================================================\n",
      "                                coef    std err          z      P>|z|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------------------\n",
      "const                         0.8979      0.246      3.654      0.001       0.416       1.380\n",
      "ar.L1.D2.Sales of shampoo    -1.2964      0.161     -8.036      0.000      -1.613      -0.980\n",
      "ar.L2.D2.Sales of shampoo    -0.9829      0.250     -3.926      0.001      -1.474      -0.492\n",
      "ar.L3.D2.Sales of shampoo    -0.7601      0.250     -3.038      0.005      -1.251      -0.270\n",
      "ar.L4.D2.Sales of shampoo    -0.4184      0.170     -2.465      0.020      -0.751      -0.086\n",
      "ma.L1.D2.Sales of shampoo    -1.0000      0.088    -11.346      0.000      -1.173      -0.827\n",
      "                                    Roots                                    \n",
      "=============================================================================\n",
      "                  Real          Imaginary           Modulus         Frequency\n",
      "-----------------------------------------------------------------------------\n",
      "AR.1            0.1735           -1.2777j            1.2894           -0.2285\n",
      "AR.2            0.1735           +1.2777j            1.2894            0.2285\n",
      "AR.3           -1.0819           -0.5168j            1.1990           -0.4291\n",
      "AR.4           -1.0819           +0.5168j            1.1990            0.4291\n",
      "MA.1            1.0000           +0.0000j            1.0000            0.0000\n",
      "-----------------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "# ARIMA(4,2,1)\n",
    "model = ARIMA(shampoo['Sales of shampoo'], order=(4,2,1))\n",
    "results = model.fit()\n",
    "print(results.summary())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f2858a5f898>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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eBwBGNFrV3MWiYJZV3Xhsagk5Dhwq2vXrdQxffft+ZHMcn/rJc8jl/fCcczw9GawrFbUQnY5hx6AT4022FFZSWeQ44LIapOAZWQrqwznHbCVLwWZCKJaW3meEPOaLRKHevmfSdQriPUIBW0JzjQq7VhQGXIIoVLuhR84EodcxXDy6vlXFpj47vvB7u/H4xCL+7YlJAMDZxRgC0eQ6y6IexnxOvOyPNvVNJ1YzuyxGWIx6DFCtQkuIxDOIp7PrMo9E3DYjsjmOKDXFq4lANAkdA/rshaJQu/uo2OIABPdRPJ3FUkxbsZ6uFQWv04JUNlf1hj49GcTeYVfZEZnvOLgR1+7y4rb7x3F6LirFE4oti3oY8zkRiqWb2qdJbJvttAips1Sr0BpmI+vnKBQi9T8iF1JNBKJJ9DlWg/delxkLy6maM+xKicKIW7hXWosrdLEoVE9LTWayeHZ6qWLAmDGGr9x8IRxmAz7+o2fx5CuLcNuM2DrgaHiNY/nBPOP+5sUVxJ2nyyqIHtUqtIZy1cwi1P+oPubz1cwiXqcF2RyvOb03EE3CbNDBZVndHK4WsGkrW49EoYIp+cJMGKlMruoozQGnGV+5eR9ePBfBT4+fw4FNvWv64dfLmE/IQBqfbV5codB9BIBqFVpEuWpmEbH/EbW6qA2h71GhKNTezUC8zoDTDMZWP9diIonWgs1dKwoDMqqaj0hFa9WDxtfv8eEPLt0g+3w5uG0m+FyWploKq+4j0VKwIp3lqk2mIwRmwwkwtvrQKobaZ9dHoNhScNXX6iKwnFzjOgKExngmg05z7qPSjvIuwOuqXt14ZDKIrQN29JWoMC3FF27aDafFiLdePKLIGgFgbMjZXFGIi+4j0VKwARAykMqlRxLK4w/HMeAwS7Uwxbjz7VLIfSSfXI5joehhLtYZBGpMSw1Ekxjtta05ptMxDPVYyH2kFRxmA2wmfdkdcS7HcXQyiEM1ZBE5LUZ84abdGHSV9gvXw06fExPz0aa10Y6WsBQAqlVQm9kScxQKcZgNMOoZQhrLdGkmoVgKmRxfY30N1Ok+mo+utxQAYFiDcxW6VhSAyjnLL89FEUk01qpCCXb5XEhnOc4srDTl+pFEBhajDmaDMAhIqlUIauuN3u5UqmYG8k3xbCaKKdRAYFnMGFr9vVqMergshprcR+lsDsGVVGlRcFsxS6KgHbxOS1kzUolWFUowlm93cbJJweZIPC2lowLCh6bfYaa0VJWpVM0s0munpni1IMYLix/mXldtVc2Ly8LvvLDFhciw2wJ/JIGMSgOx1KCrRWHAVb6Q5chkCD6XRXKntIoL+h0w6FjT4gpCh9S1oaUNHitmlsh9pBbLyQyiyUxFSwHIN8WjmIJsxNqC4uB9rQVspWoURIbdVuQ4MKfCzHe16GpRKOc+4pzjyJkgDm7pXZOC1gpMBh22eR14uUmiIHZILWSDx4pzZCmohr9KjYIIWQq1seo+KiUK8h/ipfoeiUgT2DTkQupyUbAglspiObm2dcBMKA5/JIFDCqWWNspOn7NptQrF7iNgtYCN+uyog1SjUCVBwWMzaa6lQjOZjyRhM+nXdSPwuoRmmHLbx5RzQwHAcF7ItVTw2XRRYIwdZ4x9I//nayy/9WaMXcsYu4cx9iPG2FebvY5SrE5gW2tKPn0mH09QoH+REoz5XDgfTiDchAdCOfeRUKugHZO4nZnN57nLiSmEYikSa5kElpMl6z68TjNSmZyUjl31OvnPQb/DtO57Q27tVTWrYSkscs4/lP/zUc45zwvDZwHczDl/O4AYY+yNKqxlDWIhS3G31COTQbgsBuzwOtVeUknEYPPLc8q7kMq5jwBKS1UL0VIorLwthdtmQo6vFhwSlQlEEyV397WmpQaWk3DbjFKGXiEOswE9VqMk7FpADVHQMcb+ijH2LcbYTfljOwC8xDkXn8Z3ArhGhbWsodx4viOTQRzYrEyrCiWQ2l0o3Eabcy4N2CmksICNaD6zkQT67CZYjOsfOoX02gXxpriCPMrVFtQ6lrO4KroYoYBNO5+Vplc0c85fDwCMMQOAHzHGxgH0AQgWnBbMH1sDY+wWALcAwOjoqOJrK9UUb3E5iVcCK/j9Szcq/nr14nNZ0GM1Kp6BlMzkkMrmpL5HImQpqEu1GgURj9j/iOIKsghEk3jt9oF1x1dbXci0FMqIi8iI24pz5D6qHc55BsAjAHYDWARQ6LDvzR8r/pnbOecHOOcHBgbW39xGcduMMOl1a94cYr+jQ1vaI8gMCIVLY00INotuiGL3kVCrYCJLQSWqVTOLiP2PqICtOol0FtFEpoylUL3vWSHlLA6RYbeV3EcNcAWA5wBMANjLGBN/028F8KjKawFjDANO85oCtiOTQZgNOuwbWT9Up5WIA3eUDDJKfY8s6w3GEY+NREEl/OF4TZYCzVSojlRbUMLt4zAbYDXqZbmPOOfV3UduC5ZiaawktTEAqenuI8bYtwHEATgA3Mk5n8wf/xKAHzDGVgDMAniw2WspxUBRzvKRySAu2uiGydBe2bpjQy6spLI4txTHxqLGXPUiWQpF7iNAcCG9dL65o0AJYUcbiqVlNR/0kKUgG2l8ZongPWMMXpe8WoWVVBbxdLZiEoDYGmY2HMe2NklOaQQ1YgrvK3P8VwB+1ezXr4bXacbkotBXaCWZwYnzEdz6uq0tXtV6dvpW210oJQrFA3YK2eCx4qETc8jleNsE3LWI3BoFALCb9DDpdRRTkEElSwHIF7BFqscBKlUziwwXpKVqQRTaazvcAgp3DMenlpDN8bapTyhk52A+LVXBYHPxgJ1CNnhsSGVzUlUo0RyqTVwrhDEGj91IloIMAvk4Ybn5FF6nZV0qeunriOJS/v6I904rGUgkCk7BH5jMZPH0ZBA6Blwy2l7xBACwmw3Y1GdTNAOpeD5zId2WgfRqYBnfPHxGdpWrUvirzGYuxmMzUUxBBoFoEjqGsrNQit3G5RCTUCpZCoMuC3SMREEziDuJQDSJI2eC2D3sKvmQbAd2DjpxUsFahdUBO+vdRxslUdDGG70at//mVXz5Fy/h2NSSqq87K43hlC8KZClUJ7CcRK/dDH0Z16fXZcZyMoNYqnJwWI77yKjXYdBlwfmwNtJSSRTyAaTzSwkcnw61vFV2JcaGXJhcWEEinVXketFEGgYdg7VE0dSIu3sK2DjneOz0AgDg3397VtXX9ocT6LEaYTPJC+/12slSkMN8pHIaqVTAViUtNRBNwqBjcFsrbxS1VMBGopB/c/xyfB6JdA6H2lgUdvmcyHHg9NyyItcTW1yU6gRrNenRZzd1hftocjGGc0tx9DvMuOf5WSyoGEeRW6Mg4rEbqSmeDMr1PRIpVbha8jr5GoVqyRbDbu1MYCNRyL857nnhPADgQBuLwk6F212UanFRyAaPtSsshcOnAwCA227eh1Q2hx8dnVbtteVWM4v02kxYiqWQpaZ4FalWhSy3qjmwXPk6IiNuK86HE6rHpJpB14tCn8MMHQOmg3Fs6bfLegO0ik19dliMOsWCzdFEumTmkcgGj60r5io8dnoBGzxWvGGXF1dc0Ifv/XZKtYdurZaC1BQv3hpr4aXzETxzNtSS15ZLLseri0IN7qNKhWsiQz0WpDI5LGog3tP1oqDXMSlD4WCbzE8oh17HsGPQqZylkMiUDDKLCBPYtD1XIZPN4clXFnH19n4wxvDeKzbh3FIcvxqfb/prpzI5LCwn4XPJn+4ntrpoVVzhi3efwOd++kJLXlsuS/E0Mjle0X3ksRlh1LOq7qNqLS5EVmsVOn8T1fWiAKy6kNo5yCwitrtQgkg8Dae5kqVglR5cWuW5mTCiyQyu3NYPALh29yAGXWZ8V4WA81xEfo2CiFjVvNQCUeCc4+RsBOfbvM+PnIwhxhgGHJXHcmZzHIsy3UckChpDvOmH2rBorZgxnwsLyylZhTfVEALNlSwFIQNpWsMupMcnFsAYcOVWQRSMeh3+8NAmPHoqgMmFlaa+tj9SWzoqIMQUACC4or776Hw4gWgig2iieipnK5FqC6q4fQZclQvYgisp5Hj5ArhChjU0bIdEAcC2AQc29dkwqlD7iGai5GwFYepaZUsB0HYB2+HTC9g73CPtwAHgXYc2wqBj+N5TzbUWaqlmFnHbhPvVilqFkwW9sPxtnJMvPui9VVqHCK0uyouCHItDxGMzwmLUkaWgFT55/U7c9eGrSqZmthtiBlKjLqR0NodYKluxUG9E4wVsy8kMjk2FcNX2/jXHvS4Lrt/rw4+OziCeUqYmpBT+cG3VzEBrYwqFGxG/jL5BrULuw9zrrOw+Elu8yBEFxpiQltrmrjU5kChAmB/QY2vPKuZi+hxmeJ1mnJxtTBQqNcMTsZkM+VqFzn+jl+KpVxeRyXFcva1/3ffec/kmhONp3P38+aa9/mw4AYfZUFMFvc2kh8mga42l4I/CpBceGXNtLArz0SSsRj3spsqT7LxOC0KxNFKZXOnrREQ3lDzRHu6xkvuIaA07fU68PNeY+yhaoW12ISMeq2bdR4+dXoDFqMOlJbLOLtvSix2DDnz3ybNNyz2vtUYBEHakvTYTQq2wFGYjOJgfPuUPt2/yQSCahNdlrmr5SzPayyRS1GIpAMCwWxtVzSQKHciuIRdOzS0jky29w5HDat+jyqKwwWPFOQ280UtxeGIBh7b0lRzIzhjDey7fhBfOhfHcTLgpr19rjYKIx25SPdCcSGdxZmEFl27qhcNsaGtLQW5tweoEttL/l0A0CafZAGsVi0Nk2G1FYDlZ1vKoh5OzEfzs+IxirW3kQKLQgewcdCKVyUlzIOphtUNq5Z47YgGbFio1C5kNxzExv4yrtq0bDS7xtks2wG7S4ztPTjZlDf5wQtYchWI8NqPqlsKpuShyXGi1Mugyt3WgeT6akLW7lwrYymQgVSuAK2a4xwrOlXWtPXhiDh//4XOKXU8OJAodyNiQmIFUf1xBrvtog8eKZEZ7cxUenxBGgl+1rfzsb4fZgJsv2YBfPD+LoMI+/Ew2h/lo/ZaC2jGF8XwMa2zIBV+Ppe0DzXLSSFdbXZQXhf5aRCGflqqkZT0TimHQZYalRNPKZkGi0IFs8zqg1zHpg1oPldpmF7JBoxlIh08H0O8wSSm+5XjPFZuQyijfDymwnESOAz4ZYziLaUVM4aQ/AqtRj029Ngy6LG3rPkqks4gkMrJ2+H12ExgDAhXcRzVZCm7lh+3MhOJSvZBakCh0IGaDHhf02xuyFCoN2ClEfENqSRQ45zg8sYgrt/VX7X65Y9CJy7b04ntPnVW0H1I9NQoiHrsJS/G0qk3xxmej2OlzQqdj8LksmI8m27IpXy21BQa9Dn328sN25MYmRIalWc3KCeZ0KCZtzNSCRKFDGRtyNVTAFomnwRjgNFe2FMSh5FrKQBr3R7GwnMRVJVJRS/HeKzZjOhjHo6eU64fkr3G4TiEemxGcA2GVmuJxzjHuj2BX3m3p67FILSDaDdHNKcYLquEtM4EtnsoimpRncYhYjHr02k2KuY8y2RxmwwlsJEuBkMOYz4mZUFyKDdRKJJGBw2youlO2mw3o1VitwuH8QJ2rt5ePJxRy3Z5BeJ1mfPdJ5SqcG7EUpAI2leIKc5EkQrE0xnwuAML4SaA9C9hqsRQAcUb7+v/HgiQutXVNVjIt1R9JIJvjZCkQ8hB94afm6nMhRaq0zS5Ea3MVHptYwDavQ/Yu3ajX4V2HRvHrUwFMLSpjMfnDcViMOvRUSQkuhSff/0ituII4AlZ8z4kZU+2YgTRfqyiUaXVR63VEhnusmFWogE38zFFMgZDF2JCwa6u3srnagJ1CRtxWnNOI+yiRzuLpM4uyXUci7zo0Ch1Trh+SUKNgrau1imgpqJWBVJh5BKy6vOYUaMqoNIFoEowJQWQ5eJ0WLCyvj48ExKZ6NVsKyk1gmw4KnzmyFAhZDPdY4LQY6o4rRPOjOOUgWgrtWKvw8R8+i+8/NSX7/GNTISTSuZpFwddjwfV7BvHDo9N4NVD/ONRkJosHT/hxfGqprhoFoKApnkqWwrg/ghG3VbJq+h1m6HUMc21oKQSiSfTZTTDo5T3avC4zchxYXFkrcLW6oUSG3RZEkxkpkaPmaaP7AAAgAElEQVQRZkJxMLYawFYLeVtFou1gjDU0WyGSyEhB5Gps8NiQzOSwsJxqq8l0gWgSPzt+Dnc/dx67hpy4eLT6kKTDpxdg0DFcvrV80Vo53n/VBXjwxBxe/z8fxdYBO67dPYjrdg/ioo0e6CvEZtLZHB6fWMDdz83iwRN+RJMZeGxG3HzJSM1rAApjCuoEmsdno2tSd/U6YRZBIzGF6WAMH/jOUfzDOy7CrrwFogSBaAL9NWQMrVY1J9cEpwPRJHQM6LPXbikAwOxSAi5fY/3UZkJx+FwWmAzq7t1JFDqYMZ8Ldx4/B855zW6ISDyNXVVy9EUKW2i3kygcmxLGQpoNOnz0P47jnj+7uqqP/vDEAi4edcNRJeuqFJdu8uDRT1+Dh1+aw0MvzeGbj53B/330VfQ7THj9mBdv3O3DVdv6YTXpkc1xPH0miLufP4/7XphFKJaG02zA9Xt9uGn/MF6ztQ9GmbvZYqxGPcwGnSqWQjKTxSuBZVy727vm+GBPY7UKx6ZCGPdH8fk7X8SPP3SFYh2Khb5H8i2wgbwQFM9VCCwn0Ze3iGphqGd12M5OmZ+vcrQiHRUgUehoNvXZEE1mEI6n4bbJ86GKRGpyH63WKsjZjavFsakQjHqGf3nfQfzRN5/C5376Av75Dy8u+4AJraTwwrkwPvaGHXW/5ojbive9ZjPe95rNiCTS+PXLATz00hzue8GPHx2dgcWow8HNvXjZH5W6dV67exA3XTiE1+4YUKQylTGGXpWqmifml5HJcSnzSMTnMuPVQP1tVkR/+dGzIfzs+DncfMmGhtYpEogmsc0r/2EsWQpFGUi11iiIjChY1XwuFG/J4C8ShQ5GDPj5I4maRCGX41hOZuCSG2hu06rmY2dD2DPcgyu29uGT1+3E394/jquO9ONdh0ZLnv/EK4vgHOvmJ9SLy2LEm/cP4837h5HK5PD0mSAeesmPwxMLuGijGzftH8YbdnlhMyn/MfOoVNUsBpnFGgURn8uCJ15ZrPu6U8EY+h1mbPBY8Tf3juPa3YOys+HKwTlHQOb4TJGBAvdRIbVWMxdez6BjmG1wrkI6m8NsOI6NZCkQtVCYGli8k6vEcioDzqtXM4s4zAZ4bMa2KmBLZXJ4fiaMd1+2CQDwwddegCdeWcAX7zqBSzd5sGNw/W7x8EQATrMB+zf0KL4ek0GHq7b3KyY41fDYjarUKYz7IzAbdNjcZ19zfLDHIo3lrEf0poIxbO6z4Qs37cZbvv44/tdDp/GFm3Y3tNalWBrpLK+ptsBi1KPHalxXwDYfTWJ7ifdQNfQ6hkGXpeG5Cv5wAjmufjoq0MLsI8bYuxljdzHGfsoY+3Sr1tHJiEVEtfp2I/lK2Gp9jwrZ4LG1laVwcjaCZCaHSzcJ7iydjuGrb78ITosRH/n+sXUT0zjneOz0Ai7f2ic7M6WdESyF5geax/1R7Bh0rvudNVqrMB2MY7TXhgs3uPGuQ6P49pOTDU8TrHX+gUjxBLZcjmOhRoujkBF34+3mW5WOCrRIFBhjTgDvAfAWzvnNAPYxxup39HYpUmVpjQNPpKlrNZjrI+72GrYjBpkv2eSWjg04zfiHd+zHqbllfOkXJ9acf3YxhplQHFertJNvNr12kyqWwsmizCMRXwNVzalMDufDcWzIz0T/1HU74bQY8IWfv9hQ2rPoAqpZFFxrW12E44LFUU9MARDSUht1H4kbsI0tmBvfqi3TawA8xFffAT8H8DstWkvHYjLo0Gc31fzBXLUU5IuCOGynXWoVnjkbwlCPRcr2ELl6+wBu/Z2t+I+np3H3c6ujNA9PCK0taq1PaFc8NhMiiXRDg5aqEYgmsbCclIrWChnsqc9KBYTMHM6B0fwDz2M34VPX78RTZ4K4+/nZ+te7LKyl1tYUXqdlTUxB6p/kqk8UhtxW+MOJhhoGzoRi0LH6emM1SqtEoQ9AsODfwfyxNTDGbmGMHWWMHQ0EAqotrpOop41xJG8pyK1oBgRRSKRzWGzBbOBSHJ9awiWbSmdC/fkbd+CSUTc+99MXpLYUh08vYMRtxZZ+e8mf6TTUaIonFkaWSl321WmlAkI8AVgVBQB458FR7B1x4b/f8xKWk5l6llt3wZnXaUYgmpQ2PNJ16rYUrEhnudQ/qR5mQnEM9VjrTltuhFaJwiKAwlyr3vyxNXDOb+ecH+CcHxgYkNe8rNvw9Vhq9utKlkIN7qN2aqHtDydwbimOS8qkxxr1OvzjOy8GY8BHf3AciXQWT7yygKu29SuWD99qPPbm9z8qbm9RiN1sgLPOsZylREGvY/jSW/ZiLpLE1x45Xdd65yNJWIy6mmtQBpxmpLI5SWDn62xxITKiwFyF6VBMyvpTm1aJwlMArmWrn9C3APhNi9bS0dRjKUhT12pxH/W2TwttKZ4w6i57zsZeG/72v1yI56aX8IHvHEUkkVEtM0gN1KhqPumPYNBlll6rmME6NiSAEEQ1GXTr3DyXjHrwB5duwDcPn8HEfO2tRALLQlVyrcIvFruJcYV6LQ6R1QK2+jOQZkJx1Vtmi7REFDjnSwC+A+DHjLEfAHiOcz7eirV0Oj6XBYsrKSQz8gd71+M+Wp2r0HpL4djZEEwGHfYMV04tvXHfEP7o8lE8lm+VfaVG4gmAOp1ShfYW5VOdfa76xnKKlbql2rb/xY1jsJn0+OJdJ2qOX9VbW+AtqlUIROuzOETEVhf1WgqpTA7+SKIlmUdAC1NSOef/wTn/fc75Oznnf9+qdXQ6vp7SxTeViMTTsBr1NfkrnRYj3G1Sq3BsKoQLR3pk9YT5y9/djTGfE5eMusvueDsRT5M7paazOUzML0vzwEtR71jOqWBsjeuokH6HGZ+4bicOTyzg/hf9NV13vs4q5OKqZmHGc+0Wh4jLYoDDbKg7LVUMxHedKBDKUE+tQjSRqalGQWS014azCs0TqJdkJosXz0XKBpmLsRj1+M9bX4N/+/8ONXll6tKbtxSCTbIUXg2sIJXNYVclS6HHXNdYzqnF8qIAAO++bBRjPie+/IuXEEvJDzoLfY/qEIVi91EDNQqA0IZk64Adp+frq7to1RwFERKFDqew1YVcIom07GrmQrYOOOry9SrJi+ciSGVzZYPMpbCbDQ23UGg3rCY9LEZd0ywFKfOoQgdTn6v2sZzhWBqRRKaiKBj0Onz5rXtxPpzA1381Ieu6yUwW4Xi6LkvBYTbAZtJL1vZ8pD6Lo5CdPqcUqK8V0Rrf2EuWAlEHPslSqMF9lEjL7ntUyDavA7PhRN0jQJXgeImitW6lt4lVzSdnozDqGS4YKJ/CW89YzimpUrfyLvjg5l687eIR3PGbMzizUL3xXqPB4cKq5kYtBUDoYLy4klrXfVUOM6E49DpW97yNRiFR6HB6rEaYDbqa3EeReKamzCORbV4HAOCVBrpjNsqxqRA2eKyyB7NrGU8TO6WO+yPY5nVWjDtJVmoNGUjTofXpqOX47I1jMOoZbrvvZNVzxYdvvQVnXqcF89EkkpkslmLpxkUhH4upZwjWdCiGoR5Ly9qxkCh0OIyxmmsVojXMZy5ke14UWuVC4pzjmbOhmlxHWsZjMzUtpjA+G606b8NXRzxLtBTkuEa8Lgs++LqteODEHJ45G6x47mrBWX2bhQGXUMC2uCz8Pmutii5GzNqqx4XUynRUgERBEwzWmBoYScifz1zIaK8NJr2u7gBao5wPJzAXSUpN8LqdZlkKoZUU/JFExcwjANIQmlrdR712k+yY1p9evQUDTjO+cu94xRTVeSXcR5FEw24okV67CV6nGeN1NPmbadFwHRESBQ3gqyE1kHOOSFz+gJ1CDHodtvTb8UqLLIVjZ8WiNRIFAOi1Nad99sm8y6NaO3a9jsHrNNfU6mI6GKtpRoDNZMDHrt2Oo2dDeOilubLnBaJJMAb0OepLO/Y6LVhJZTG5KLhGlZgwuNPnrNl9lMxkMRdJtizzCCBR0ASi+0hOsU8inUMmx+vOxtnmdeB0i0ThmbMhWIy6qjvYbsFjNyGSyCjeFG91sE71GR211ipMB2M1d/58x4GNuGDAjr974OWy/9fAchK9NlPdvYJEd9FL54WHuBKisGvIhdPzyzXdn3NSOipZCkQDDLosSGZyspqjRfKZQ/W4jwBBFKaDMSTS8iuoleL4VAj7N7hb0iSsHRGrmpcUboo37o+g32GS9WCspao5m+OYCcVlBZkLMeh1+PT1Y5iYX8ZPnpkpec58pLGMITFA/eL5MACgz66ApTDoRCqTk6wPObSyZbYIfbo0QC297etpm13INq8DOY6G5vPWQyKdxYnz8ovWuoFmVTWP+yu3tyjE12PBnMwkh9lwHJkcr1kUAOD6PYO4ZNSNf3j41LoBSkDjaaRiNtuJ8xF4bEZZ1fLVEC3akzUEm2fIUiCUYDC/y5GTgRSRBuzUZylsH8xnIAXUdSE9PxNGJscpnlCAVNWsoChksjm87C89WKcUgy4LoskMVmS0uy7VHVUujDF89k27MBdJ4luPn1n3/YU6+x6JiO6jpVhasXTnbV4H9DpW00S56VAMhvxIz1ZBoqABaml1EamjQ2ohW/rt0DFgYk7dDCQ5nVG7DY9duIdKFrBNLsaQzORKtssuhdh7S46VOi2lo9bnGjm4uRfX7hrEN379yhoh5JzX3QxPxG0zwpR3SyoRTwAAs0GPC/rtNQWbZ0JxDLut0JdoFqgWJAoaoJaxnKuzFOqzFMwGPTb12VUPNh87G8LmPhv6Gmw/oCWa0Sl1tb2FfEsBgCwX0nRQqNQdamCa2F/csBMrqQy+9svVmQvheBqpbK6hHT5jTBIDpUQBEGZR1JKWOhOKtay9hQiJggaoZSxnpI75zMVs86rbA4lzjmNTS+Q6KsLTBPfR+GwUeh2TqterUUs8ayoYw4jb2lCl7vZBJ95+YCP+/bdnJctDqdqCpoiCz4mZUFx2a5iZUBwb3K0LMgMkCppBbmpgPQN2itnmdeDMwgrSTZwPXMh0MI6F5SQFmYuwmvSwGvWKBprH/RFsHbDDbNDLOr+WhoyVWmbXwsffuAN6HcPfP/gygILCtQatSDGu0Oh1ChFjM6dkuFsT6SwC0WRLg8wAiYJmkNvqIhLPwKhnMDeQXbHd60Amx1Vro70aTyBRKKbXrmyri5NVBusUYzMZ4LQYZLqPlHGNDLoseP9VW/DzZ8/jxXPhhvseiYg/3+h1Ctnpk5+B1A7pqACJgmaQaylE8n2PGplVvE3qgaROsPnYVAh2k176gBGreOxGLCkUaA7H0zi3FK+5OFBOrcJKMoPFlZRiD7wPvm4rPDYjbrtvXDH3kRiTUNJSGHFb4TQbZAWbxZbZZCkQiiB3LKcwYKex2QJbB9RtjPfM2RD2b3S3NCOjXfHYTIrFFMTUyUqDdUrh67HAX6V1ey3dUeXgshjx0ddvx+GJBdz57DmYDTo46xyfKSK6wrwKpoMyxjA25JSVltrq4ToiJAoaQe5Yzkg8XXc1s4jdbMCI26pKBlIslcG4P0pN8MrgsZkUyz6SM1inFIOu6gVsU4vKigIAvPvyUWzwWHHifARel7kh6xcAfu/CIfzjOy/C1gozJOpB6IEUrdqGZjoUg0mva7hDa6OQKGgEubUKkTrbZhejVgbSc9NhZKlorSy9duUshZOzUbhtRqkYUi4+lwWB5cpjOaWW2Qrugs0GPT51/U4Ayrh8bCYD3nLRSMPiUsyYz4VoIoPzVYRzJhTHiMcKXYstYhIFjSA3C0TokNqYpQAIovBKYBm5Gufz1ooYZL6YitZK4rGZEE1kFMkEG/dHMOZz1vxQHOwRxnIuVBjLOR2MwWk2wG1TdizqTRcO49DmXuwb6VH0ukoiZiCNz1aOK8yE4i2PJwAkCppByhevshuJJjKKWArbvQ4k0jmcW4o3fK1KHDsbwtYBO9y2+loiax2xqrmRTDDOOf7Pr1/B8amlutx0ct5706E4NvbaFN+F63QMP7jlcvzVW/Yqel0l2SGKQpW4wkywtXMUREgUNILcsZyRROMxBWA1A6mZA3c45zg+TUVrlbj8gj7YTXq88/bf4uhk5elkpcjmOD7/8xfxt/eP4/cuHMKfvWF7zdeQU8CmVI1CKVrtbqmGy2LEiNtaURRiKSE7q9VBZoBEQTOIYznnKgSaU5kcEumcYjEFoLkZSJOLMQRXUlS0VoEdg0787MNXwmHW4113/Bbff2pK9s/GU1l88LvP4N9/O4UPvvYC/NM7L5ZdtFbIYD7JodyGJJfjmA7GMNrX+gdeq9g15KzoPmqHOQoiJAoaotpYTiWqmUXcNhP6HWacnmueKDyTn7RGmUeV2THoxM8/fBVes7Ufn/vZC/jcz15AKlM5xrCwnMQ77/gtHhmfw5fesgeffdOuunfc/XYzDDpW1n0UWE4imcnVNHFNa4z5XHh1YaVsyni7pKMCJAqaotpYTrHvkRLuI0CIKzSzhfaxqRCcFgO2Dcjrw9PN9NiM+NYfH8SHXrcV339qCn94x28xHy39Xng1sIyb//cTGJ+N4Bt/dCnee8Xmhl5bJ47lLPPem2qwO6oW2OlzIpvjZS1rsY6jHYSTREFDVBvLudohVZkMkG1eBybmlmWNAa2HY2dDuGiju+19xu2CXsfwmRvH8LV3XYwXz4fx5q89jueml9ac88zZIP7L/3kCy8kM/uOWy3H9Hp8irz3YU35DMt3AHAWtIHadLVfENhOKw2zQKdqMr15IFDREtbGcjc5SKGb7oAPRZKZiHKNeook0Xp6LUpC5Dm7aP4z/vPU10OsY/uD/PimNsLz/RT/+8I6n4LIa8dNbX6Po79bnKt97ayoYA2PASBvsglvF5j47TAZd2WDzTCiGEY9V8eyseiBR0BDVskCiYttsBeoUAEhunWYEmx+fWADnwGUX9Cp+7W5gz3AP7v7oVbh01INP/vg5/PG/Po1bv/cMdg258NNbX4PN/cpW7Qq9t0pvDqaCMfhclrqC2FrBoNdhu9eBk2WCzUKNQntYUg09HRhjfwng2lLX5ZxfxRj7PIBLAfjzx7/FOX+aMdYD4HYAHIAdwEc452cbWQtRMAUrnCjZ6VJ0HzmVch8NrqalXrW9X5Fritz/oh8emxGHNpMo1Euv3YTvvv8Q/vu9J/Gvj0/ijbsH8U/vvBhWk/IPZ1+PBcvJDJaTGTiKehAJ3VHb44HXSnb6nDh8eqHk96aDMextkwK8RreMYQBf4Jz/RjzAGBsG8Pn8P/UA/p5zfrjo5z4J4A7O+cOMsR0A/hrAexpcS9dTrdWF5D5SKNA84DDDZTEobimkMjk8Mj6PG/b4GhrIQgg71P//pj143xWbsbHX1rSmgoUFbMUDeqaDccU3DZ3ILp8LPz12DsGVFHrtq8WYy8kMQrG0oi1AGqHRT9wsgDOMsc0AwBizAdgC4JH89xMA3sEY+2fG2JcZY2L7wUOc84cBgHN+CoAy0a4uR2z9W24sZzSRgY4BdpMyosAYw/ZBp+KN8Z58dRHRREaxICgBbO63N7XLbLkNSSKdhT+S6Oogs4jYkry4jXY71SgACsQUOOfTAJYZY3YAGzjnjxd87zbO+Uc55x8BcALAZ2p5XcbYLYyxo4yxo4FAoNGlap5qYzkj8TQcZoOi2TzbvQ68orAoPHDCD5tJT7vLDkLqvVUUbBbz70kUVgfujBcN3BGzszQjCnlSEFxRlZ4OdwPYn/+6uLKmZE4j5/x2zvkBzvmBgYGBxlfZBVQathNRYJZCMdu8DiyupBTr1JnNcTx4Yg7X7PTCYuzewGSnUS7JYVqqUWiPB14rGXCY0Wc3rUtLXR2u0x7C2bAoMMZcALZyzsMAkoyxsTKnvg7AkfzXzzDGrs3//A4AZAYoRKWxnFGF2mYXonS7i+NTISwsJ3H9XnIddRJWkx4ui2HdhoQK11ZhjOVnK6x1H82E4rAYdeh3tEfTx0ZFwQbg9Zzz4wDAOV/MH98PSO6fOxhjtwO4HsDf57//dwDexxj7DoCvAPhsg+sg8lS0FOIZxaqZRZRujPfACT9Meh2u2UmWYadRakMyHYzBYtQpOuKykxnzufDyXHTN7AkxHbUdahSAxrOPrgGwlTH2saLjYwA+zzm/HULq6Ro450ugbKOmUDiWszgvPJJIK75jG+6xwmbSK2IpcM5x/wk/rtzWp1jaLKEepTYkYnfUdnngtZoxnxOJdA5TwRi25GtFpkPt0TJbpCFR4Jz/iVILIZShcCxnsQBE4sq7j3Q6hq0DykxhOzkbxXQwjg//zjYFVkaojc9lwam5tRbjVDDWNqmW7YCUgTQbkURhJhRvq8p9SgLXGJVqFaKJjGLVzIVsV2g05/0n/NAx4NrdgwqsilAbX48FgWgSmfwUOM45Fa4Vsd3rhI6tDtyJJNIIx9NtZSmQKGiMcmM5szmOaDLTFLfMVq8Ds+GE1Jq7Xh484ceBzb3oJ/9zRzLosiDHgYVlIRMtFEtjJZWldNQCrCY9NvfZpWDzuTZqmS1CoqAxyo1GXBb7HikcaAYESwEAXgms1H2NyYUVjPujuIEK1jqW4rTUKeqOWpKxIaeUltpuNQoAiYLmKDeWU+kOqYVIGUhz9WcgPXBCaI913R5yHXUqxQVskih08cS1UuwcdOFsMIaVZEYq7msnFxuJgsYQx3L6izpWKt33qJDRXhtMel1DA3fuP+HHvpGetjKjidoojme14y64HRgbcoJz4NRcFDOhOGwmPTy29sm2I1HQIIMuC+aK3EeRuOg+Uv7NZ9DrsKXfjok6R3PORRI4PrWE68lK6Gj67CYY9WzVfbQYQ7/DDJtCvba0wphvdeCOmI7aTim7JAoaxOeyYC6qnvsIENpo19sY78G86+gGqmLuaISxnKu1CtOhGEapvcU6NnpssJn0GPdH22qOggiJggYpNZZTGrDTpKKwbQMOTIdiSKRLDyavxAMn5nDBgB3bvM4mrIxQk0GXWRIFsXCNWItOt9ruYiYUa4u5zIWQKGiQUmM5VwfsNMeU3z7oAOfAKzXGFZZiKTz56iJlHWkEcUOSzuZwfineVgHUdmLM58Rz02FEExmyFIjmU6pjpeg+apYo1NsY75GT88jmOM1O0AiC+yiJ80tx5Hh7ZdW0E2M+F+J5q7rdAvEkChqkcCynSDSRgd2kb9oksy39duhY7aJw/wk/hnosuHBDe4wiJBpDHMt5Mj8zgNxHpRFnKwDtJ5wkChqkVKuLSDzd1CZzZoMem/rsNYlCLJXBb04FcP0eX1tlXxD1I1qpRyaDAEgUyjFWIApkKRBNp9RYzkgi3ZS+R4Vs89aWgfToywEkMzkqWNMQgwWiYNQz6d/EWtw2E3wuCxxmA3qalBFYLyQKGsRkEAZ2rIkpxDNNyzwS2eZ1YHJhBels8WC90jxwwg+PzYhDm3ubui5CPcSq5hPnI9jgsTV1LnSns39jD7Z5HW1nJVNViUYp7m0fTaabPuhku9eBTI7j7OJK1fTSVCaHR8bnccMeX9PiHIT6iO6jbI63na+83bjt5guRzsnbQKkJfRo1is+1dgpWJK78fOZitueFQE5c4clXFxFNZKhgTWOIYzkBUOFaFTx2k+TqbSdIFDSKt8hSiDRhPnMxW73C0JDTMtpdPHDCD7tJjyu39Td1TYT6iC4kCjJ3JiQKGqVwLCfnvGkDdgqxmQwYcVurNsbL5jgePDGH3xnzwmLUVzyX6DzE4DJNXOtMKKagUQrHcvbaTcjmuCpzj7d5HXh8YgF//sNnwQHkOAfnkL4GB1ZSGSwsJ6lgTaOIcQWKKXQmJAoapbBWwaAXshua7T4CgN/dN4SJ+WU8PRkEY4COMTAILb2Fv4WvL9vSizeMeZu+HkJ9ht1CLIFEoTMhUdAohWM5RQuh2e4jAHj7wY14+8GNTX8don35o8s3Yc+wq+3y7wl5UExBoxSO5YxKfY/oQ0o0nwGnGdeRa7BjIVHQKIVjOZs5dY0gCG1BoqBRCsdySlPXyJwnCKIKJAoaRhzLGW1y22yCILQDiYKG8bks8EcSiDR56hpBENqBREHDCO6jBCLxNEwGHRWKEQRRFRIFDTPosiCVyWE6FCMrgSAIWchyMjPG/hLAtaV+nnN+Vf6cNwD4NwCHOOez+WM9AG6HUNBqB/ARzvnZcscb/L8QRYhpqafmlinziCAIWch9UoQBfIFz/hvxAGNsGMDn81+7ARwE8EsAhT6KTwK4g3P+MGNsB4C/BvCeCscJBRFbXUwurGDPCI27JAiiOnLdR7MAzjDGNgMAY8wGYAuARwCAc77EOb8Nws6/kEOc84fz55wC4KtynFAQsdVFJsfJUiAIQhayYwqc82kAy4wxO4ANnPPHG7i+rNdljN3CGDvKGDsaCATkLpXIU9irnWIKBEHIodZAcwqCy0nuIN7isUK8yvG1Bzm/nXN+gHN+YGBgQP4qCQCrYzkBdfoeEQTR+cgWBcaYC8BWznkYQJIxNibjx55hjF2b//kdAAJVjhMKI7qQyFIgCEIOckXBBuD1nPPjAMA5X8wf3190XgZAtuDffwfgfYyx7wD4CoDPVjlOKIyYgUQtLgiCkINcn8I1ALYyxj5WdHwM+QwkAOCc/2nhNznnSyiRVVTuOKE8g/kW2tTigiAIOch6UnDO/6TZCyGag4/cRwRB1ABVNGucVfcRWQoEQVSHREHjXDBgBwD4XNYWr4QgiE6Ato8a58DmXvzyE6/DBQOOVi+FIIgOgCyFLoAEgSAIuZAoEARBEBIkCgRBEIQEiQJBEAQhQaJAEARBSJAoEARBEBIkCgRBEIQEiQJBEAQhwTgvOcqg7WCMBQCUmuPcA2FcaCXUPKcd16T2ukcBTLXZmjr1d6n2mpS6d/S7VH9Npe7dAgBwzm+Q8fMCnPOO/gPg9nY6px3X1IJ1B9pwTZ36u1R7TYrcO/pdtmRNVe+dnD9acB/d3WbnqP167bjuJYWuI/e8djtH7ddTck1K3Tv6XZE+xGoAAAW+SURBVKq/Jjn3riod4z4iOgfG2FHO+YFWr4OoHbp3nYtS904LlgLRftze6gUQdUP3rnNR5N6RpUAQBEFIkKVAEARBSJAoqARj7L4K33svY+xdaq6HkA/du86E7lt9kCioR6UhyToAerUWoiSVPngaQnP3ju5bZ943oPn3jkRBRRhjn2eMXVHwby18MCt98DSDBu8d3bfOpan3jsZxqosea3cnmvhgMsb2AngPhP+bE8CnOOcRxthjAE4CSALoA/DHnPNU61baEJq7d3TfOpdm3juyFFpLR5qvJfADyEH4wG0A8Ib88REAt3LOPwrgeQDXtWZ5TUEL947uW+fStHtHoqACjLFeCL1LwgCG8sdGxa81wB0A7uSc/1cA9wGw54+/yjnP5r/2A3C3YnGNoPF7R/etc2navSP3UZNhjH0WwBUA/geACQB35H2cWQhKjvzX2dJXaF8KPni9nPOn8offAOA/W7cq5dDqvaP7BqAD7xugzr0jUWgynPOvFB36vRLnfFel5ShG0QdvlDH2bQApAK8CECsi0wU/0nEfQi3eO7pv0jkddd8A9e4dVTQTBEEQEhRTIAiCICRIFAiCIAgJEgWCIAhCggLNhCwYY3oAfwXgAM+P9mOMfRzAAQBRACEA/41znmOM7QfwNwCWAcQA3MI5TzPGPglgJ4Tc6gXO+Sdb8F/pOhS6d38GYB+EZ4YOwIc558vq/2+6CyXuXcG1PgPg96vOXFBifBv90f4fAG+FkPnwcP7fOwB8q+D71wN4c/7reyCkzAHAnwL4QInr/QuA3a3+f3XDnybcuz8B8MFW/7+64Y9S9y5/nbeL16n0h9xHhCw453dyzp8sOJQA4GSMsfy/PQCuYIxZAGQ458H88TsBXFPikg4As01bMCGh5L1jjOkAXAqhlQLRZJS4d4yx3QD2cc5/JOc1yX1E1AXnfIox9kMA32SMhSEUCdkA9GLtrNhg/pgEY+xtAI5yzkNqrZdYpZ57l38I3Q7gMgA/4pz/Rt1VE0Dt944x1gPgVgAfk/saJApE3XDOfwLgJwDAGPtdAGYAixB2LyK9EN6gyJ93NYCrOOefUHGpRBG13jsu+CA+kD//s4yxN3PO71J10QSAmu/dDfmvv543LsYYY/+Lc15WJEgUiIZhjDkAfALAeznnScaYiTHWmzdl3wrg0fx5l0Hwa/7X1q2WKETuvSsiDsCl5jqJ9ci5d5zzHwL4YcHPPFxJEAASBaJ2pDa8jLEvA+gBMADgy5zzmfy3Pg3BvI1CaOH7EcaYFcBdAO4FcHt+1/Jtzvljai6+y6n33pkBfAeCe8IAIRb0T2ounKjv3pW4TrLaC1GbC4IgCEKCso8IgiAICRIFgiAIQoJEgSAIgpAgUSAIgiAkSBQIgiAICRIFggDAGFthjL23xPFfMMa+2cB17yn4+r56r0MQakGiQBACTwF4c+GBfM+YeQD6Bq5rLvja2MB1CEIVqHiNIARyAB5njF1dUFD3QQj9fj4EAIyxYQC3QWhL3APge5zzXzDGvgigDwAD0A/g+5zzuxhjtwHYyRj7GoDPCJdgX4PQ1GwbgE9zzk+r9j8kCBmQKBDEKt8E8I8AHmOMOSG0cpgp+P7/gFBBOp5vEHcvY+xw/nvHOOf/yhgzAngAwF2c888wxg5wzj8KSB1Gv8w5n2eMXQng/RDEgiDaBhIFgsjDOY8wxkKMsU0AbgLwr0WnDHLOx/PncsbYsxB2/ABwOn88zRjLlXmJLOd8Pv/1OQjWBUG0FRRTIIi1/G8AHwZwdYn20HOMsTFAaiW9H3kxqACr83sE0RLIUiAIgRQAcM4nGGMXQHABAUA2/wcAPgXgK4wxMabwdc55mDFWeA4ApAu+Ps0Y+waArxcdL/4ZgmgLqCEeQRAEIUHuI4IgCEKCRIEgCIKQIFEgCIIgJEgUCIIgCAkSBYIgCEKCRIEgCIKQIFEgCIIgJP4fYBpLUc6/RuYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.resid.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f28582e6e10>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.resid.plot(kind='kde')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count     34.000000\n",
       "mean      11.226048\n",
       "std       66.730384\n",
       "min     -110.457557\n",
       "25%      -35.653924\n",
       "50%        8.525816\n",
       "75%       57.335824\n",
       "max      156.402102\n",
       "dtype: float64"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.resid.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rolling Forecast ARIMA Model\n",
    "\n",
    "ARIMA 모델로 미래 데이터를 예측하기 위해 predict() 함수를 사용합니다. 이 함수는 파라메터로 예측할 타임스텝을(steps) 필요로하는데 학습 데이터에대한 인덱스 상대값을 입력하면 됩니다. 가령 모델을 학습하기 위해 100개의 학습데이터를 사용했다면 다음 스텝 예측값의 인덱스는 start=101, end=101 이 됩니다. 예측 결과 리턴값은 하나의 예측값을 포함한 배열이 됩니다.\n",
    "\n",
    "또는 forcast() 함수로 파라메터 없이 다음 한 스템의 데이터를 예측할 수 있습니다. \n",
    "\n",
    "데이터를 train 과 test 로 나눈 뒤 train 데이터로 모델을 학습시키고 test 데이터의 각 시점에 해당하는 예측 해봅니다. 그러기 위해 새로운 actual value 를 하나씩 수집하면서 그와 함께 앞선 시점의 데이터로 ARIMA 모델을 학습과 예측을 반복하는 rolling forecast 를 수행하게 됩니다.\n",
    "\n",
    "아래 코드에서 수동으로 관측값을을 history 변수에 추가해가면서 모델링과 예측을 반복하면서 prediction 과 expected value 를 출력하고 최종적으로 그에 따른 mean squared error (MSE) 를 계산합니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predicted=399.145200, expected=342.300000\n",
      "predicted=354.296566, expected=339.700000\n",
      "predicted=429.967876, expected=440.400000\n",
      "predicted=392.634689, expected=315.900000\n",
      "predicted=420.191849, expected=439.300000\n",
      "predicted=397.585316, expected=401.300000\n",
      "predicted=487.892625, expected=437.400000\n",
      "predicted=434.160085, expected=575.500000\n",
      "predicted=467.057786, expected=407.600000\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/lyle/anaconda3/envs/tsa/lib/python3.7/site-packages/statsmodels/base/model.py:508: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  \"Check mle_retvals\", ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predicted=568.082759, expected=682.000000\n",
      "predicted=468.024731, expected=475.300000\n",
      "predicted=687.491691, expected=581.300000\n",
      "predicted=617.839224, expected=646.900000\n",
      "Test RMSE: 68.519\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "from math import sqrt\n",
    "\n",
    "X = shampoo['Sales of shampoo'].values\n",
    "\n",
    "# train , test 데이터를 2:1 로 split\n",
    "size = int(len(X) * 0.66)\n",
    "train, test = X[0:size], X[size:len(X)]\n",
    "# 학습시킬 데이터\n",
    "history = [x for x in train]\n",
    "predictions = list()\n",
    "# test 데이터만큼 모델링 & 예측\n",
    "for t in range(len(test)):\n",
    "    model = ARIMA(history, order=(4,2,1))\n",
    "    model_fit = model.fit(disp=0)\n",
    "    output = model_fit.forecast()\n",
    "    # predicted value\n",
    "    yhat = output[0]\n",
    "    predictions.append(yhat)\n",
    "    # actual value\n",
    "    obs = test[t]\n",
    "    # actual value 를 다음 스텝에서 학습할 데이터에 추가\n",
    "    history.append(obs)\n",
    "    print('predicted=%f, expected=%f' % (yhat, obs))\n",
    "error = mean_squared_error(test, predictions)\n",
    "print('Test RMSE: %.3f' % sqrt(error))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "실제값(파란색)과 rolling forecast(red) 결과를 비교해보면 트렌드를 어느정도 예측하고 있음을 확인할 수 있습니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f2853a435c0>]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(test)\n",
    "plt.plot(predictions, color='red')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "tsa",
   "language": "python",
   "name": "tsa"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}