Arima_Test_3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ede9685a",
   "metadata": {},
   "source": [
    "## ARIMA with Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "785afe2e",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Aaron\\anaconda3\\envs\\mlenv\\lib\\site-packages\\ipykernel_launcher.py:3: FutureWarning: The pandas.datetime class is deprecated and will be removed from pandas in a future version. Import from datetime module instead.\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "from pandas import read_csv\n",
    "from pandas import datetime\n",
    "from matplotlib import pyplot\n",
    "from pandas.plotting import autocorrelation_plot\n",
    "from statsmodels.tsa.arima.model import ARIMA\n",
    "from pandas import DataFrame\n",
    "from statsmodels.tsa.stattools import adfuller\n",
    "from pmdarima import auto_arima\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from math import sqrt\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9f5ac90",
   "metadata": {},
   "source": [
    "### Read the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d1ad4a6a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DATE\n",
      "2000-01-01    4.0\n",
      "2000-02-01    4.1\n",
      "2000-03-01    4.0\n",
      "2000-04-01    3.8\n",
      "2000-05-01    4.0\n",
      "Name: Rate_Overall, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "series = read_csv('Resources/overall_monthly.csv', header=0, parse_dates=True, index_col='DATE', squeeze=True)\n",
    "print(series.head())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c7226bf",
   "metadata": {},
   "source": [
    "### Plot the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "156482af",
   "metadata": {},
   "outputs": [
    {
     "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": [
    "series.plot()\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b35e2608",
   "metadata": {},
   "source": [
    "### Auto-Correlation Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "558c16bb",
   "metadata": {},
   "outputs": [
    {
     "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": [
    "autocorrelation_plot(series)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "fc35bfca",
   "metadata": {},
   "outputs": [],
   "source": [
    "series.index = series.index.to_period('M')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f5516fe",
   "metadata": {},
   "source": [
    "### Fit the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e93ec267",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                               SARIMAX Results                                \n",
      "==============================================================================\n",
      "Dep. Variable:           Rate_Overall   No. Observations:                  264\n",
      "Model:                 ARIMA(0, 1, 0)   Log Likelihood                -276.737\n",
      "Date:                Sun, 20 Mar 2022   AIC                            555.474\n",
      "Time:                        20:03:10   BIC                            559.046\n",
      "Sample:                    01-31-2000   HQIC                           556.909\n",
      "                         - 12-31-2021                                         \n",
      "Covariance Type:                  opg                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "sigma2         0.4803      0.004    110.357      0.000       0.472       0.489\n",
      "===================================================================================\n",
      "Ljung-Box (L1) (Q):                   0.21   Jarque-Bera (JB):            374579.88\n",
      "Prob(Q):                              0.64   Prob(JB):                         0.00\n",
      "Heteroskedasticity (H):              89.15   Skew:                            12.25\n",
      "Prob(H) (two-sided):                  0.00   Kurtosis:                       186.25\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n"
     ]
    }
   ],
   "source": [
    "# fit model\n",
    "model = ARIMA(series, order=(0,1,0))\n",
    "model_fit = model.fit()\n",
    "# summary of fit model\n",
    "print(model_fit.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e661d494",
   "metadata": {},
   "source": [
    "### Plot the Residuals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "92a81ab7",
   "metadata": {},
   "outputs": [
    {
     "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": [
    "# line plot of residuals\n",
    "residuals = DataFrame(model_fit.resid)\n",
    "residuals.plot()\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6feb32ab",
   "metadata": {},
   "outputs": [
    {
     "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": [
    "# density plot of residuals\n",
    "residuals.plot(kind='kde')\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a6205e59",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                0\n",
      "count  264.000000\n",
      "mean     0.014773\n",
      "std      0.735448\n",
      "min     -2.200000\n",
      "25%     -0.100000\n",
      "50%      0.000000\n",
      "75%      0.100000\n",
      "max     10.300000\n"
     ]
    }
   ],
   "source": [
    "# summary stats of residuals\n",
    "print(residuals.describe())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6d38f5c",
   "metadata": {},
   "source": [
    "## Rolling Forecast ARIMA Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "c9e77abf",
   "metadata": {},
   "outputs": [],
   "source": [
    "# evaluate an ARIMA model using a walk-forward validation\n",
    "from pandas import read_csv\n",
    "from pandas import datetime\n",
    "from matplotlib import pyplot\n",
    "from statsmodels.tsa.arima.model import ARIMA\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from math import sqrt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "99f5af27",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "            Rate_Overall\n",
      "DATE                    \n",
      "2000-01-01           4.0\n",
      "2000-02-01           4.1\n",
      "2000-03-01           4.0\n",
      "2000-04-01           3.8\n",
      "2000-05-01           4.0\n"
     ]
    }
   ],
   "source": [
    "# load dataset\n",
    "#def parser(x):\n",
    "#\treturn datetime.strptime('190'+x, '%Y-%m')\n",
    "series = read_csv('Resources/overall_monthly.csv', header=0, parse_dates=True, index_col='DATE')\n",
    "print(series.head())\n",
    "#series.index = series.index.to_period('M')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2ee90e0",
   "metadata": {},
   "source": [
    "### Split the Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a3a9eced",
   "metadata": {},
   "outputs": [],
   "source": [
    "# split into train and test sets\n",
    "X = series.values\n",
    "size = int(len(X) * 0.66)\n",
    "##size = int(len(series) * 0.66)\n",
    "train = X[0:size]\n",
    "test = X[size:len(X)]\n",
    "history = [x for x in train]\n",
    "predictions = list()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fbdcc4d",
   "metadata": {},
   "source": [
    "### Validate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "270a143d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predicted=6.100000, expected=6.200000\n",
      "predicted=6.200000, expected=6.100000\n",
      "predicted=6.100000, expected=5.900000\n",
      "predicted=5.900000, expected=5.700000\n",
      "predicted=5.700000, expected=5.800000\n",
      "predicted=5.800000, expected=5.600000\n",
      "predicted=5.600000, expected=5.700000\n",
      "predicted=5.700000, expected=5.500000\n",
      "predicted=5.500000, expected=5.400000\n",
      "predicted=5.400000, expected=5.400000\n",
      "predicted=5.400000, expected=5.600000\n",
      "predicted=5.600000, expected=5.300000\n",
      "predicted=5.300000, expected=5.200000\n",
      "predicted=5.200000, expected=5.100000\n",
      "predicted=5.100000, expected=5.000000\n",
      "predicted=5.000000, expected=5.000000\n",
      "predicted=5.000000, expected=5.100000\n",
      "predicted=5.100000, expected=5.000000\n",
      "predicted=5.000000, expected=4.800000\n",
      "predicted=4.800000, expected=4.900000\n",
      "predicted=4.900000, expected=5.000000\n",
      "predicted=5.000000, expected=5.100000\n",
      "predicted=5.100000, expected=4.800000\n",
      "predicted=4.800000, expected=4.900000\n",
      "predicted=4.900000, expected=4.800000\n",
      "predicted=4.800000, expected=4.900000\n",
      "predicted=4.900000, expected=5.000000\n",
      "predicted=5.000000, expected=4.900000\n",
      "predicted=4.900000, expected=4.700000\n",
      "predicted=4.700000, expected=4.700000\n",
      "predicted=4.700000, expected=4.700000\n",
      "predicted=4.700000, expected=4.600000\n",
      "predicted=4.600000, expected=4.400000\n",
      "predicted=4.400000, expected=4.400000\n",
      "predicted=4.400000, expected=4.400000\n",
      "predicted=4.400000, expected=4.300000\n",
      "predicted=4.300000, expected=4.300000\n",
      "predicted=4.300000, expected=4.400000\n",
      "predicted=4.400000, expected=4.300000\n",
      "predicted=4.300000, expected=4.200000\n",
      "predicted=4.200000, expected=4.200000\n",
      "predicted=4.200000, expected=4.100000\n",
      "predicted=4.100000, expected=4.000000\n",
      "predicted=4.000000, expected=4.100000\n",
      "predicted=4.100000, expected=4.000000\n",
      "predicted=4.000000, expected=4.000000\n",
      "predicted=4.000000, expected=3.800000\n",
      "predicted=3.800000, expected=4.000000\n",
      "predicted=4.000000, expected=3.800000\n",
      "predicted=3.800000, expected=3.800000\n",
      "predicted=3.800000, expected=3.700000\n",
      "predicted=3.700000, expected=3.800000\n",
      "predicted=3.800000, expected=3.800000\n",
      "predicted=3.800000, expected=3.900000\n",
      "predicted=3.900000, expected=4.000000\n",
      "predicted=4.000000, expected=3.800000\n",
      "predicted=3.800000, expected=3.800000\n",
      "predicted=3.800000, expected=3.600000\n",
      "predicted=3.600000, expected=3.600000\n",
      "predicted=3.600000, expected=3.600000\n",
      "predicted=3.600000, expected=3.700000\n",
      "predicted=3.700000, expected=3.700000\n",
      "predicted=3.700000, expected=3.500000\n",
      "predicted=3.500000, expected=3.600000\n",
      "predicted=3.600000, expected=3.600000\n",
      "predicted=3.600000, expected=3.600000\n",
      "predicted=3.600000, expected=3.500000\n",
      "predicted=3.500000, expected=3.500000\n",
      "predicted=3.500000, expected=4.400000\n",
      "predicted=4.400000, expected=14.700000\n",
      "predicted=14.700000, expected=13.200000\n",
      "predicted=13.200000, expected=11.000000\n",
      "predicted=11.000000, expected=10.200000\n",
      "predicted=10.200000, expected=8.400000\n",
      "predicted=8.400000, expected=7.900000\n",
      "predicted=7.900000, expected=6.900000\n",
      "predicted=6.900000, expected=6.700000\n",
      "predicted=6.700000, expected=6.700000\n",
      "predicted=6.700000, expected=6.400000\n",
      "predicted=6.400000, expected=6.200000\n",
      "predicted=6.200000, expected=6.000000\n",
      "predicted=6.000000, expected=6.000000\n",
      "predicted=6.000000, expected=5.800000\n",
      "predicted=5.800000, expected=5.900000\n",
      "predicted=5.900000, expected=5.400000\n",
      "predicted=5.400000, expected=5.200000\n",
      "predicted=5.200000, expected=4.700000\n",
      "predicted=4.700000, expected=4.600000\n",
      "predicted=4.600000, expected=4.200000\n",
      "predicted=4.200000, expected=3.900000\n"
     ]
    }
   ],
   "source": [
    "# walk-forward validation\n",
    "for t in range(len(test)):\n",
    "\tmodel = ARIMA(history, order=(0,1,0))\n",
    "\tmodel_fit = model.fit()\n",
    "\toutput = model_fit.forecast()\n",
    "\tyhat = output[0]\n",
    "\tpredictions.append(yhat)\n",
    "\tobs = test[t]\n",
    "\thistory.append(obs)\n",
    "\tprint('predicted=%f, expected=%f' % (yhat, obs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b7465f23",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test RMSE: 1.161\n"
     ]
    }
   ],
   "source": [
    "# evaluate forecasts\n",
    "rmse = sqrt(mean_squared_error(test, predictions))\n",
    "print('Test RMSE: %.3f' % rmse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "07312d87",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/QUyg9K6E0gI/JglwIYQtPF6r9E6EcFyDmCAn8xwvCXAhhC3cXo2zsi1wORuzUiTAhRC28FiVH8SMDg+jbmw4K7b7TuJp1szMA9+1qwoqDR0S4EIIW3i8uvR5mFDhQUyAi09pwC8rdpF90A3XXGP2FB81qgoqDR0S4EIIW3gsi7CSJ9JDhVvgANemp1LosRi/ZBu0aQNnnAEjRpiDIUS5JMCFELbweHWlu1AA2jWKp23DOMbO32ouDBgAq1bB7Nk2Vxo6/ApwpdSDSqm/lFLLlVJjlFKRdhUmhAgubqvyg5hF+pyeyoodB1i+LRuuvRZiYkwrXJSr0gGulGoE3Aeka63bAU6gr12FCSGCi8dr4SrbB36cAd67fSPCwxymFV6rFvTpA2PHQk6OzdWGBn+7UMKAKKVUGBANyPZhQtRQHq8+ch74cQxiAsRHu7i4XX3GL9lGgdsLt90GeXkmxMURKh3gWuttwOvAFmAHkK21/qXs85RSA5VSC5RSC7KysipfqRDihObvIGaRa09PJafAw6TlO6FrVzOgKd0o5fKnC6UO0BtoCjQEYpRSN5Z9ntZ6uNY6XWudnpSUVPlKhRAnNI+l/e5CAejaNJHGCdF8OX8LKGUGM+fMgb/+srHa0OBPF0pPYKPWOktr7QbGAd3sKUsIEWxMF4p/g5gADofi8g4NmbNhLzkFbrjR1y6cONGmSkOHPwG+BeiqlIpWSingPGClPWUJIYKN23cmpnlQ+QAH6NC4NgArd+RAcjKkpcHixf4XGWL86QOfC3wDLAKW+b7XcJvqEkIEGY/l/yBmkXYN4wHMdEKAjh1h0SJ/Sww5fs1C0Vo/o7U+SWvdTmt9k9b6kF2FCSGCizmVvsQgpsNh/lRCvbhIkmpF8FfR3iidOsHatXDggE3VhgZZiSmEsIXHKrMSs5LdJ0XaNozjr+0lWuAAS5f69T1DjQS4EMIWRwxi+hng7RrGszYz18wH79TJXJRulFIkwIUQtnBbZQYxbWiBey3N6p050KAB1K8vA5llSIALIfzmtTRaU/pUen9b4I18A5nbZSDzaCTAhRB+c3stgNKzUCo5A6VISp0o4iLDSg9krlgB+fl+fd9QIgEuhPCb1zJ7drtKnkrvZwtcKUXbhvH8VTSVsFMn8Hph+XK/vm8okQAXQvjN4zUBbmcXCkC7RnGs3JljWvhFM1GkG+UwCXAhhN/clulCsXMaIUDbhvEUeizWZ+Wa1Zi1a0uAlyABLoTwW1EL3FkFLXCA5dsOmI2tOnWSmSglSIALIfxWFYOYAE3rxhLlcpZe0PPnn8VL9Ws4CXAhhN+qYhATwOlQtGlQi7+2lZiJcuiQOStTSIALIfzn8fWB2z2ICWY++IodB7AsLSsyy5AAF0L4ze0t0wK3McDbNowj95CHzXsPQsuWEB0tAe4jAS6E8FtVDWKCmYkCMGNtFjid0KEDTJ0KhYW2fP9gJgEuhPBb0TTCsCpogbdpEEd6kzoMnbiCKSt3wV13wbJl0LdvjR/MlAAXQvitqAXuKtkCt2EWCpiBzJH9T6dNgzjuGr2I6Z0vhGHD4Lvv4OabzerMGsqeOyyEqNE8ZVvgNs1CKRIX6eKzWztz3YdzGThqAc9cdgWdHtpN6zefZ/dBN4m33IA52RE4+2yoU8e21z6RSYALIfzmqcJBzCK1o8MZPaAzfYfP4bFxy8DVlfvOvIGHvv8cvv+2+Int2sHChRAebuvrn4gkwIUQfqvKaYQlJcZGMGHQmWZpPcB9Z/LIp1ewYeNO3r+xE8nrV8Gtt8LLL8PTT9v++ica6QMXQvjNfXgWStW1wItEupy0bRh/+M8Dd/6DVfWb8+g6J/qWW8zg5vPPm61nQ5wEuBDCb8VdKPYPYh5LSp1oBl90EtPXZPHd4m3w9tsQFwe33RbyA5wS4EIIv1X1IOax3NS1Cac1qcO/Jq5gd3S8maUyeza891611RAIEuBCCL+VO42wGgPc4VC8ctUpHDzk5cGxSzjUpy/84x8wZAjMm1dtdVQ3CXAhhN+OaIFXc4ADtKhXi6GXt2XG2t0MGrME9wfDzUHIF14IS5ZUay3VRQJcCOE39+ETeQIX4AB9Tm/Mc73a8suKXTwwIxPP5F9Nf3jPniF5FFtQBPisdbsZNWczhR4Ldu+GESNgw4ZAlyWE8PEc3g/cAZZl/lTTIGZZ/bql8cTFbfjhzx38c3421uRfISLChPjq1QGpqaoERYD/sGwHr305h88v7Ie7SZoZXW7dGu68EzIyAl2eEDWex7cfeJhTmQFMCEgLvMjtPZrxyAWtGLd4G48vyzchrjWcey6sXx+wuuzmV4ArpWorpb5RSq1SSq1USp1hV2ElPb9jBgs/uZP+v43m59SO3H/X2+y5qT+MHAktWpg5n1pXxUsLISqgKMBdDkfxBlMBDHCAe89tyaBzW/Dl/K08t9aL/vVXcxjEuefC5s0Brc0u/rbA3wYmaa1PAtoDK/0v6UiqsBDXWWeiFy4k/NuvmZ/alp5pV7N+5mK4/HJ46il45pmqeGkhRAV4Sh6pdoIEOMBD57fi9rOa8unszby4xYn++WfIzjYhvm1boMvzW6UDXCkVB/QARgBorQu11vttqqu0+++HCRNQnTpxQdv6jBnYlfAwB31+3sG6YcNNl8rQofDCC1Xy8kKIv1dqEPMECnClFI9f3Iabz2jChzM20mZ8Jn2ufJa8jB14GjdBx8RATAwkJsLo0YEu97j5M8rQDMgCPlZKtQcWAvdrrfNKPkkpNRAYCNC4cePKvVLRLmM+TRJj+Py2rvQdPpsbRs7jqxfeoElBATz5pBmseOSRyr2OEKJSPJaF06HMjoAnUICDCfFnL2tLy+RabN17EEjji1NTcHw1lrgIJ5e2b0jUvDnQrx+Eh5PT6wqUUsRGhJnB2F27oEGDQL+NcvnThRIGdALe11p3BPKAIWWfpLUerrVO11qnJyUl+fFypbWoF8vnt3Wl0GNx/cgFZLz5LlxzDTz6KLzzjm2vI4Q4No9Xl55CCAGbhVIeh0NxU9cmPH5xGx6/uA23P3A1bT57nye79+OqpleQ/b8f8ZzRDeu663n85qH0GzEXfvgB0tMhJQUWLAj0WyiXPwGeAWRoref6Hn+DCfRq07p+LUYN6EJOgZvrP17IzvdGQO/eMGgQ1gfD+XXFLjbv8f1CsHYtTJhQneUJUWN4LF28D8oJMAulIrq1qMsHN53GusxcrvxsCWf1eJilyS14c9xLPD20P1x6qekvj4yE4cMDXW65Kh3gWuudwFalVGvfpfOAat/+q12jeD4b0IW9eYVc/8lCMj/6lKyzzoW77uTHf77CvS+O48D1N0ObNtCrl5mxIoSwlcdrlV6FCSd8gAOc07oe793QiYx9+bRt3YjIKT+jOnSgXt4+vr/nWVi1Cq69FsaMgdzcQJd7BH9/xxkEfK6UCgc2AP39L+n4dUitzcf9T+fmEfPo8fYs9On3MGbHPl7/6W28kxxoFAcG3EFc7n546il2exTvdLqcKzs14tTECPjgA3NA6qOPHtHfLoQ4NrelS+8FDkER4AA9T05m+XMXFv8GMXcOL45ZzPT1e7kAB5EDBsAnn8DXX0P/gETcUfkV4FrrJUC6PaX45/S0BEbcks6wyWu5Or0dpz4zDcftt3EgshZ9657DgboNeOPKdkRu2E3H557Eee4mvo+MoM3Cb3Ht2mm+ya5d8PrrEuJCHCeP1zqyDzxIAhxKbIML4HTSp0saE5bv4pcVu+jVvbtZODhiRGgF+ImmW/O6dGtet/jC2LHUBl7fls31H87huo8XEPt/9zIOD0/99hEAixq3JfHbETSZ9jO8+SZERR21m2XC0u18OmsT793QiXoFB+D66+G662DAgKp/c0KcwDxefWQXygk0iHm8ujVPJKVOFGPnb6FX+4bmlJ/Bg02XykknBbq8w4JiKb2/2jWK54vbu3LfeS35bcj5tPr9R3juOXZ9NZ67Bw7jyr9crHt8KAwcaOaSDx16xPf4adkOHhi7hAWb9/HK6JlmX4UpU2DQoJBamitEZQTjIObfcTgU15yWysx1e8zUw5tvBqfTrP4+gdSIAAcT4g+d34p6cZFmrvjTT5N8TW8+H9gVpRS9353Fm1c8QOGNN5mz9C64AOaaCTa/rtjFoDGL6ZBam0c716Pf0Dvxrl4Dn35q/pEOHChL+UWN5rGCuwulPFenp6AUfL1gq9mW9rLLzM980fs7AdSYAD+a5kmxfHvXGZzTuh7//n0DnZv2ZdrAIRyavxC6dmVz955MHvwK926dxejwVdz96n20ydrEQ32eIvvq6+DVV+G33064/zMLUZ3cXm12IoSQCfBGtaPo0TKJrxdm4LW06SrNzISJEwNd2mHB20lloyaJMbx7Qyfu2pbNW5PX0K/wTGJu6cQtCydwx7xxvHJoinniaMDlYvt/P2bihgQiflzBq7ffbqYYPfywOQGkYcOAvhchAsHjtXAF4TTCY7m+S2PuGLWQp/+3nOcvvRDVuDHcdx906ABNmwa6PAnwkto1imfELaeTeaCAArcFXEJ23htEH8oubl3Urk2ThAQGTlrF+7+vJz0tgas/GI6jQ3sz0DFqFNi44lSIYOCxdOkT6SGoBzGLXHByMnee3Zz/TltPeJiDp//3P9S558J558G0aZCaGtD6anwXSnnqxUXSODGaxonRpDZOIqxlC2jWzPxJSADg/vNa0j4lnn9+8yeXTtrFqkefQU+ebJ7z1FOwf39g34QQ1cjttUqfhwkh0QJXSjH4otb0757GxzM38cqOSLOj4Z49JsR37AhofRLglRTpcjLu7u4M69OBvEIPFxWewr2PjyKrR08zDbFpUzOjJScn0KUKUeW8li59Ij2ERICDCfGnLz2ZG7o05r/T1vOZOwkmTYLt2+H88wM6qCkB7genQ3F5x0b8+tDZvHTlKSyOTub0U27jn09+yr70rmZ3xGbN4I03ID+/yuqwLG0GWYp4vVX2WkKUJxQHMUtSSjG0dzu6NE1g+PQNWF26mokLf/0FP/0UsLokwG3gcjq4rnNjpj56Ds/1asvUyIZ0PO1enntiJDknn2q2t23eHN5915wIAuQXehk+fT2nDZ3MeW/8zqxPvkOffbbZm/jhh81o9zEUeiw+n7uZbi//Rr+R87AWLjIb8MTFwcKFVf22hTjMY1m4QmwaYVkOh+LGrk3Ytj+fmet3w5VXmumFI0YErKbgH2U4gUSEOenXLY1r01P5bPYm/jvNxcdnPMQ93fsw4OeRJNx7L/kvvMSiPrczLktxIN/NLfWiOGPqeNJXz2dvXAKes86j3rBhZn+W+++HIUOgVq1Sr+PxWoxfsp23p6xh6958/s+bxdWffYRj9UyoUweio82Up/nzK/xDtCM7nwK3RdO6MeYHcPFiM9IeHm7/jRIhx+MtZxAzxAIc4IK2ydSOdvHl/K2c1TLJ7CH++uumLzwAe4ZLgFeBqHAnd5zdnOu7NObjmZv4cHoY7/Z8krNaLObhGaPoPuxZupd4vk5MZPmDT/JwYjdW51i83f8Beo//EF58EaZOhZ9/hlq1sCzND8t28Nava9iQlcf54Qf4euU4kid8S0FEFO/3uIErRr1O/UVz4Ior4LXX4PHH/7bWndkFvDN1LWPnb8Vye3g6ezHXTfqE8C2bTD/+M8/ADTeExIwCUXXcXqt4JWYIzUIpKyLMyeUdGvHF3C3syyukzq23wiuvmAU+Q444DqHKKV2NKwjT09P1ghN0Y/SqlFPgZvOeg+aB1sRtWkdqtMOcXgLQsiXExlLosbj784X8ujKTV686lWu3LYSrr0Z3785vb3zMa39ksGpnDt3D83h5xf9IGT8WFR4OgwaRMeAezh+1gm7NE/moXzrq2mvREyYw4bMfqdW+Hee0SkL9/jusWAE33MDusCje/309o+ZsBsvLvwpXcsHY90nI2Miy5OasuvgarljyC2GLF0GrVqb7p2fPgN1DcWI757WptE+tzdt9O8KwYfDgg7B3r/mNMMSs3HGAf7w9g6cvPZlbz2wKPXrAzp2wenWVbYSnlFqotT5y40CtdbX9Oe2007T4ewVuj75pxFydNmSiHr84Q694a7j2KIee0aS97vvYF3p93/7aCg/XOjxc60GDtN6x4/DXfjh9vW4yeKIeO3+LHv3dHL0/qpaem3KyvuqGV/SfrTppbRb864Ox8fqN/7tFt33oaz3y0bf0oZPbms+1batzvvhKv/TDCt3i8R907//M0Ae//Err1q3N6/30UwDvjDiRdXtpin5o7BLz4NVXzb+nnJzAFlWFev1nhr7wrWnasiytP/nEvN9p06rs9YAFupxMlQA/AR085NF9P5itmwyeqJsMnqifu2aItpQy/7nCwrQeOFDrLVuO+DqP19K93vnj8Nf995YnD4f2npja+tnzbtdX3fKm/rX56VqD9kZEmM+3aKH1559r7fEc/l4/L9+hmz/2g776/Zk6b2em1h06aB0ZqfWUKdV5K0SQ6PzCZD34m6XmwQsvmH9XBQWBLaoKjZ6zSTcZPFEv2bJP69xcrWvV0vrmm6vs9Y4W4KHXSRUCosKdfNQvnRd+XMlJ9WvR5/SLUJefAtOnm0Mnmjcv9+ucDsWb17bnnd/WcU16Ct2aXQzJbqhTh+g77iJ1+R4KMnNp9NIA2LQCx/Dh0L27GYgp0195Qdv6DOvbgfvGLOa279fz0Q8/EXVBT7jsMqwff4Ju3Uq97mEOh+ynXgOVu51sCA5iFrmsfUOGTlzBl/O30v7KU8zW0p99Bv/+N8THV1sd0gcu/tZ3izN46KulaA118/Yx9ovHaL434+hfUL8+PPYY3HGH2fVR1AinPvszV3ZK4dlebc36hxdfNCe6h7CHv1rKxD+3c995Lbk1PIuoM7uZXUxffRXat7f1tY7WBy4tcPG3ruiYQmJMBEu27gdgao+x7PzlOxwe08pyeyyWb88mv9BL86RYzt/5FzH332+mVj31lNkfxukM4DsQ1cFjlTmVPoRb30UevbA1+w8W8trPqxkZ7eLdex6ny+h3UR06mHM0n3/eTFCoQhLg4ph6tEqiR6uiDbpawjXdSn2+0yEPn87axNPT1jO4TS++vbOAdu+9avZJnz7dnCcoIR7SPFaJlZgeT40I8PrxkYy45XQWbdnHm7+soe/Bbjz0US/uWzLBzMSZPh02bDCnfFURWYkp/BYbEcY9/9eCqY+cQ1rdWK5ZG828L34wLZDRo013Soj/Ol3THbGdbA0I8CKdGtdh9G1duOSUBgxftp/sx5+BH380Uws/+qhKX1sCXNgmMTaC0bd1oUHtSPp/Mp9FN91tulFGjDBHz8mpRSHJsjSWpvSp9DUowIvce24Lcg95+GTWJjM3vEcP0x/u2z6jKkgXirBVUq0IvritK32Gz6bfiHl0bHIJfS7ayCXvvce6SdM5GB0LgFMpGtaOpHZ0OArgrLPMRvkltg1YlpHNF/M2065RPNe0jCf8/XchKwseeADS0gLx9kQ53L7frkrNQgnBVZjH0qZBHD3bJDNy5kYGnNWU2CefNIOan30Gt99eJa8pLXBhu/rxkXxxe1fS0+pwoMDDh5fcwReXDMBrWUTkHiAi9wDWvn1sWreddWsyyNu63cxcaNoUXn+dNRt2cceoBVz2zh/8OHs9W4Y8S35qY3jySfR775mVoXffDdu2BfqtCmDrXrPTZlKsb9bRxo0B2RfkRHDvuS3Iznfz+ZzNZuVy587w0kvFW+zaTKYRioA45PHy5bytvDN1HVk5h+icuY77pn3GmRsWUegIw+MMI8zpwOV1o9xu5rfpwnOdryO6cUNeXTWBJt+NQTmdJsiHDIF69QL9lmqsbxZm8MjXS/nlwR60qhttls/feCO8916gSwuIm0bMZeWOA/wx+FwiJ/0IvXqZVvhNN1X6ex5tGqEEuAio/EIvXy3YSsY+s1dM6vIFnLJ4Bm2SY4l0Oc3CoF690N27M2n5Tt6cvIa1mbmc7crlhT/H0WjiN1iRUey99Q6ir+9DTJRv98S4OLMXu6hyT45fxvjF21n6zAU4V66Adu3MzKN+/QJdWkDM27iXaz+YzbOXncwt3dKgY0coKDB7h1dyNpYEuAgJXksz8c/tvDV5DZv2HKTZngzunzmGy1ZOx0GZf8sXXwxDh0KnToEptoa49D8ziI9y8fltvkMOBgyAlSvhpJMCXVrAXPvBbDZk5THlobOJ/2G8mRf+9ddw9dWV+n5VtpBHKeUEFgDbtNaX+vv9hPg7Toeid4dGXHJKA2at30O++zR4oDcz1q/hrynzWLJ1PzERYVwXk8Pp4z5GnXaa2Xj/X/+Ctm1Zl5nLlr159GiZRFjhIXOaSufOkJIS6LcWlArcXlbtyOGOs32/7cyda5aSt2oV2MIC7OlLT6b3uzN58ceVvHLllWa72Uvtj0c7horvB1YCcTZ8LyEqJMzpKLG4CGhbn7N79WDp1v28OXkN167JIu2eHry1fSodvh4J333Hou7/4NGTe5NRqx73bJjKHX+MJTJrl1nyf9ddpi89OTlwbyoILd+WjcfSdEj1bRs7dy506WK6vmqwdo3iue2spnwwbQO9OjSk+803V8nr+HWXlVIpwCVA1c5WF6KC2qfW5tNbO/P1nWeQnFKPK5LOp+e9n/BBl6s4ec4Ufv3obv789A7u/+7fLI2oy7P9hzKr60VYb/+bQ03S2HTOReg+faBPHzP1a8cOtNZ8OH0Dk5b7TiBftAgGD4aDB22pedeBAl7+aRVTV2Wa80xHjTL7yVTh/GG7FG2x0CG1NuTlwbJlJsAFD/ZsRVpiNI+NW0Z+YdWcU+tvC3wY8E+g1tGeoJQaCAwEaNy4sZ8vJ0TFnJ6WwJcDuzJr/R4+mrGBnV2fJa/Na0S9O4zINWvw3nc/O5PbsmTWZma0PZOUrldx3S+f0WLZX+zbEE5CTDhs2oSeOZNhT3zA28sOoBR83D6Mc+7qC/v3myCfMAEiIytV457cQ+aU89mbKXR72DZ8Fqf/+S2xG9aaJ6xeDWPHntCLYhZv3U+j2lEk1YqA6XPNilsJcAAiXU5evupU+g6fw5uTV/PEJSfb/hqVDnCl1KVAptZ6oVLqnKM9T2s9HBgOZhCzsq8nxPFSStG9RV26t6hbfHHYMACcQG+gd8fivm/rxRsZ/O2ffL0wg39e1Jq71TY8F17ERQ/ezMHXP2P/+s2ceus95NeuRdRjj5kul6uugu++O66zQ7MPuvlwxgZGztxIQaGHx/VGbvjhQ6L+Wsbauo1x/3sEJ+tccybqTTfB55+fsHvJLNmynw6Na5sHc+eaj507B6yeE03XZolc36UxI/7YyCWnNjS/qdjInxZ4d6CXUupiIBKIU0qN1lrfaE9pQlQvh0Px8lWnUui1eHXSaua0SsJ7+ZN8Mu5fPP7WfbB9O3vDw7mk93M8eOE/6O6KJuGhQeRfeTURw97CUbSZU2KimcYI7M49dPjXZyvvIL9P+5Mx87eSe8jDPfH5DPj1UyIXLYDmzTn40cc8eCCNtbvyeff6TqQ/l0vtZ57goAoj+sWhxYXWr1+lGyRVVGZOAdv259O/e5q5MGeOmbqZlPS3X1fTDPnHSew/WEhcpP2rU22ZRuhrgT9yrFkoMo1QBAOP12LQmMX8tHwnV3ZsxGvRGTivuhISEsj95VdumL6fpRnZANyy4HuenTK89DeIjmbvrXfwUttL+HpTAZHuAm5c/CN3zfmGxPwDpZ+bmgpPP23mTLtc7Mk9xHUfzmHNrlwA7p31JY/MGF36a1JSYNq0gM9z/+WvnQwctZBv7zqD05okmLp69IAvvghoXaGoSueBS4CLUOP2WszdsJeuzRLMNqlLlpiWdWoqOQVufluVidtrfnZiZ//Bkj+WkJVTSGqdSLpvWsJpMydxMDySdT170XreVKJ2Z7LzjLPxXHU1KXV9Q0axsWZqWZmDL/YfLGTq6ky8vg0ccyb8yPL5qzizZV0ub5OIeuIJ87XTpkGTJuXWvy+vkOlrs/Ba5lC95Pkz6RCWT0yErxXYqpXffdWvTlrF8OkbWP7chURm7jQBPmyY6foRtpKFPEJUIY/X4rvF23h7ylp25x7i4QZu+v38MeHfjzcbdT3/vGmdVoLWmhd/XMmHMzYysEczHks+iOrZ0/wPZdo0aNTo8HMPFLj5aMZGRv6xkdwCN+dsWMjDM0Zxyq71pb+pUmZ5942V7/G8/sM55BR4mDDoTBg3zowHzJ4NXbtW+nuK8smJPEJUoTCng2vSU7miYyM8ljbbANzdC3JzISbGr3NClVI8fnEbDnkshk/fwMaTk+k4+B1u/dcd5KZ3Y/0pZtBQa03GvnzqeyzeT4iiY3YGsYvm426SxsoX3+b+jFga1o5i2LWnUvuh+6BfP7IKNR/WTyenwIPTXchpv42n4cZVxe/LoWheL5baUb6ZMN27w/XX43U4+TMjmys6+v7nMXeumS3ToUOl36c4ftICFyJIWJbmhR9X8v3S7QC037Scp8a/QUxB8Xz0MKciJiIMl0NB7dpm693+/SE8nFnrdtP/k/m0qBfLG5e0IOKyS0hZ/ScPXj6YZKuA26aOpkF2Jvui4/E6zKwXy5cPES4nscrCuW8vtG7N9geH0H1DIq9f25GrTkuBc84x8+Lnzavmu1IzSBeKEILfV2cy8LOFFHot6ngKmDDhX6Ss+dN8snNn09XTs+fh3xj25hXywfT1fDprE26PxY07F3PLpBE03bmJ7bXqUrdhXcKdDlizBu68E/7znwC+u9AlAS6EAGDamixmrMni1jOb0pBDZhbM+eebAdWjdPVk5hQw4o+NbN17EGV5OW3OZLou+4M2ybHmQA6nE554Ak45pVrfS00hAS6EEEHqaAFes3ecEUKIICYBLoQQQUoCXAghgpQEuBBCBCkJcCGECFIS4EIIEaQkwIUQIkhJgAshRJCq1oU8SqksYHMlv7wusNvGckKB3JPS5H6UJvfjSMF6T5porY84KaNaA9wfSqkF5a1EqsnknpQm96M0uR9HCrV7Il0oQggRpCTAhRAiSAVTgA8/9lNqHLknpcn9KE3ux5FC6p4ETR+4EEKI0oKpBS6EEKIECXAhhAhSQRHgSqmLlFKrlVLrlFJDAl1PdVNKpSqlpiqlViql/lJK3e+7nqCUmqyUWuv7WCfQtVYnpZRTKbVYKTXR97im34/aSqlvlFKrfP9WzqjJ90Qp9aDv52W5UmqMUioy1O7HCR/gSikn8C7wD+Bk4Dql1MmBraraeYCHtdZtgK7APb57MASYorVuCUzxPa5J7gdWlnhc0+/H28AkrfVJQHvMvamR90Qp1Qi4D0jXWrcDnEBfQux+nPABDnQG1mmtN2itC4Evgd4Brqlaaa13aK0X+f6eg/nBbIS5D5/6nvYpcHlACgwApVQKcAnwUYnLNfl+xAE9gBEAWutCrfV+avA9AcKAKKVUGBANbCfE7kcwBHgjYGuJxxm+azWSUioN6AjMBZK11jvAhDxQL4ClVbdhwD8Bq8S1mnw/mgFZwMe+bqWPlFIx1NB7orXeBrwObAF2ANla618IsfsRDAFe3jHZNXLuo1IqFvgWeEBrfSDQ9QSKUupSIFNrvTDQtZxAwoBOwPta645AHkHePeAPX992b6Ap0BCIUUrdGNiq7BcMAZ4BpJZ4nIL5VahGUUq5MOH9udZ6nO/yLqVUA9/nGwCZgaqvmnUHeimlNmG61M5VSo2m5t4PMD8nGVrrub7H32ACvabek57ARq11ltbaDYwDuhFi9yMYAnw+0FIp1VQpFY4ZiPg+wDVVK6WUwvRtrtRav1niU98D/Xx/7wf8r7prCwSt9WNa6xStdRrm38NvWusbqaH3A0BrvRPYqpRq7bt0HrCCmntPtgBdlVLRvp+f8zBjRyF1P4JiJaZS6mJMn6cTGKm1fiGwFVUvpdSZwAxgGcV9vo9j+sG/Ahpj/sFeo7XeG5AiA0QpdQ7wiNb6UqVUIjX4fiilOmAGdcOBDUB/TCOtRt4TpdRzQB/MLK7FwG1ALCF0P4IiwIUQQhwpGLpQhBBClEMCXAghgpQEuBBCBCkJcCGECFIS4EIIEaQkwIUQIkhJgAshRJD6f7Gk6LVy0Np4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot forecasts against actual outcomes\n",
    "pyplot.plot(test)\n",
    "pyplot.plot(predictions, color='red')\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36f8757b",
   "metadata": {},
   "source": [
    "### Predictions ???"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "308b4cc0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ??"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "mlenv",
   "language": "python",
   "name": "mlenv"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}