Arima_Test_1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ce2caac9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Rate_Overall\n",
      "DATE                   \n",
      "1/1/2000            4.0\n",
      "2/1/2000            4.1\n",
      "3/1/2000            4.0\n",
      "4/1/2000            3.8\n",
      "5/1/2000            4.0\n",
      "6/1/2000            4.0\n",
      "7/1/2000            4.0\n",
      "8/1/2000            4.1\n",
      "9/1/2000            3.9\n",
      "10/1/2000           3.9\n",
      "11/1/2000           3.9\n",
      "12/1/2000           3.9\n",
      "1/1/2001            4.2\n",
      "2/1/2001            4.2\n",
      "3/1/2001            4.3\n",
      "4/1/2001            4.4\n",
      "5/1/2001            4.3\n",
      "6/1/2001            4.5\n",
      "7/1/2001            4.6\n",
      "8/1/2001            4.9\n"
     ]
    }
   ],
   "source": [
    "# line plot of time series\n",
    "import pandas as pd\n",
    "from pandas import read_csv\n",
    "from matplotlib import pyplot\n",
    "# load dataset\n",
    "series = read_csv('Resources/overall_monthly.csv', header=0, index_col=0)\n",
    "# display first few rows\n",
    "print(series.head(20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5f71374f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iA5qtjan0gMenUSSAC0PQWvPYR6mMGTyI1feew/0Lxp+Uszyd+RMjMZsUP35jNwp4985ZXD59GAAXxNonl0lH5sBmazUO3NfRAq/18I2NJYUiDKGgoo7M4mpWLJ3Y/PW2s0L9vfjjVVPYl1vORROGEB3ix4plccQPDeKC2MG88OUPZBZXM7uXyi48X1s5cMDjVySUAC4M4aBjyN+4IQHdev5l04ZxGcOa7wf6WLnlnJE0NtnwMpv43pEPFwOT1pw0DvxECsWzx4JLCkUYgnPM9pghg1x6XYvZxOwxYWxIz0Nrzx5xIHqPfTGrE/d9DJJCkQAuDCEjv4JAHwsRg7xdfu3F8VFkl9SQeqzc5dcWxmDTbY9CqfXwFIoEcGEIGXmVjB0S0OmOy66YP3EIZpPi073HAXuH5lPr9lFe28Af139P+nEJ7P2dvRPzxH2jtMAlBy4M4WB+JfMnDumVa4f4e7Egbggrtx/hR2cN58H39rLraAnr0/I4XFjF6j3HWXffeR49Hlj0TOst1ZpHoXh4DlwCuPB4RZV1FFXVM2awa/PfLT2+JI6vDxSy+K9fU9doI25oIGnHy5kYFUh6Tjkzn9qE1Wxi4tBA/n3zWb3yTUC4h7Pvw4jjwCWAC4+391gZAHFDg3rtNSKDfHjlxgQ+3nOcMRGDuHrGcP7zzVF+lDCcL/fnsyuzhGMlNWw+UEB6TnmvlkX0Leds+ZNHoTiGEUoAF6JnkjJLMSmYHN27QfPsUWGcPerE2ip3nj8agCvOjOaKM6MprqrnrN9uZF1KrgTwfqTtFrgxUijSiSk8XlJmCeMjA/H3dm97I9Tfi5mjQlmbkiNDDvuR5ha4AVMoEsCFR7PZNMlZpUwbEezuogCwKD6KQ4VVHHCsZCiMT2OP4C37NbzMJpSSAC5EjxwqrKSitpFpw4PdXRQAFsRFohSsTclxd1GEizi/TLUcB66UcuzKIwFciG5Lc4zBnhwd7N6COEQEeDMjJpR1qRLA+wubdrbATz7uY4Bt1SSAC4+WkVeJ2aQYGe7v7qI0WzwpigN5laQdL3N3UYQLnGiBn3zcx+L526pJABceLSO/gpgwP7wsnvNRXTZlKCF+Vn71USpNHr5ji+iYrXkUyskR3MdLUihC9EhGfiVjB3dvBcLeEuLvxYplcSRllvJh0jF3F0f0UHt/g30skkIRotvqGps4WlTNWBevQOgKy6YM5YwwPz7Zc9zdRRE91UYnJtiHEkoLXIhuOlJYTZNN9+oU+u5SSrEwPpLtBwspra53d3FED7TXienvbaGirtENJeo8CeDCY2Xk2zdZ8LQUitPi+CgabZqH3t/LjkNF7i6O6Kb2cuDRIb4cK/HsrfYkgAuPdbigCoBREZ4zAqWlydFBnBUTwpf7C7hl5Xdke/gvu2ibMwXeehRKdIgfhZX1VNd7bitc1kIRHiuzuJrBAd5d3gOzryilePfO2WQVV7PgL1u46sVvGBzo0/y4WcFPLhzL3PGD3VhK0RFnC7x1DmVEqB8AWcU1jI/0zG+BPWqBK6V+ppRKU0qlKqXeUkr5dPwsITons7i6+ZfIkw0P9eO5q6cxPjKAYF9r87+88jp+9nYyhZV17i6iOJ12xoEPbw7gnvvNqtstcKXUMOAnwEStdY1S6h3gamCli8omBrjskhrOHhnq7mJ0ykUTh3BRqw0nMvIquOS5rfx5wwF++z+T3FQy0RFbO6NQnI2HTA8O4D3NgVsAX6WUBfADZEyVcIn6RhvHy2qINkALvD1jhwQwd3wE2384tYMzs6ia+kbPHmM8UDSPQml1PMTPir+XmSwP7tvodgDXWh8DngUygRygTGu9vvV5SqnblVKJSqnEgoKC7pdUDCjHS2vQGkOkUE5n2ogQDhdWUVJ1YqhhUmYJc5/9kn9vP+K+golmJzoxTw7hSimGh/p5dAql2wFcKRUCXAqMBIYC/kqp61ufp7V+SWudoLVOiIiI6H5JxYDi/No6PMTXzSXpGecyuMlZpYD9m8WD7+3FpmHH4WL3FUw0s53YkucUw0P9+m0K5SLgsNa6QGvdAHwAzHZNscRA5/zaOiLM2C3wScOCMCl7qxtg0748MvIriQ7xJTmrRDaG8ABtLSfrNCzYl5yy2j4uUef1ZBhhJjBTKeUH1AAXAokuKZUY8DKLq/EymxgSYOyBTf7eFsZHBvLmziwq65rIK68lzN+L/z1nJCtWp5NdUtM82kG4h3NDh9ajUACCfK1U1DbSZNOY2zrBzXqSA98BvAfsBlIc13rJReUSA1xWcTXRIb6YPPCXpqtunhNDVJAPr207zJqUHC6OiyQhxj66ZrejZS7cp60t1ZyCfK0AVNQ29GGJOq9Ho1C01k9orWO11vFa6/+ntZYBr8Ilsor7T8v0RwnD+eSeOVwYa5/Qs3hSJLGRAfhazew+KgHc3XQ7U+kBAh0BvLzGM2djylR64ZEyi6sZHmrsDsyWlFI8feVknlg6kdmjw7GYTcweHcaG9Dwam2yU1XhmC28gONECPzWAO1vgnvr+SAAXHqespoGymgbDDyFsLWyQNzfPGdmcS100KYrjZbUse34bc5/5krxyz+0s6890O+PAQQK4EF2W1TyEsH8F8NbmTxiCxaRIzymnpLqB+1Yl8fZ3mTQ2yQSfvtTeOHDw/AAui1kJj+Nc1a+/5MDbE+RnZUFcJAUVdSyeFMmTn6bz7aFi/LwsLJ0y1N3FGzDaWw8cINDXHiIlgAvRSc6JE0YfA94Zz187DZsGs0lx+ZnRXPDsZj5LzZUA3odsji887Q0jBCjvj6NQhOgNmcXVBPlaCfSxursovU4p1ZwTD/SxsjB+CF/sz6em3rO38upPnOPA2+rE9LWasZqVx7bAJYALj5NVXNPvOjA7a3F8FDUNTXyWluPuogwYuv2Z9CilCPK1SgAXorOy+tkQwq44e1QYE6MC+e2a/XyfW8HRoiqP3hGmPzjdVHqwjwWXAC5EJ9hsekBPLzebFM9cNZnS6noW/GUL5z/zFZf/fbu7i9WvNe+J2U40DPSxUu6hAVw6MYVHyauopb7JNmBTKABxQ4P46O45HMirYOvBQj7YfYyiyjrCBnm7u2j90on1wNtugQf5Wimtrm/zMXeTFrjwKFnFNUD/HwPekfhhQVw+PZqrzxoBnFiOVriecxx4OxkUyYEL0VnNQwgHcAu8pUnDgjCbFEmZpe4uSr91urVQQAK4EJ2WWVyNUjA0eGB2Yrbm62VmQlQASVmy6FVvOd1qhGAP4OW1jR65drsEcOFRsourGRrki5dFPppO04aHsCerTKbY95KOR6FYaLJpyms9bzSQ/JYIj9LfViF0hTljwqisa2SnbMHWK9rb1NhpYlQQADsOnbo5tbtJABce5UhR9YDvwGzt/HGD8bWaWZsqk3t6gz7NcrIAZ48KJdjPytoUz/v5SwAXHiOnrIbCyjrihwW5uygexdfLzLzYCD5Py6PJpvk+t4LP03IprJT9U1zhRCdm249bzSYunjiEjfvy+WJ/HnWNnrPMgQRw4TGcIy2cO7mLEy6ZNJSCijp+u2Yfi/66hTv+u4tfr053d7H6hdNt6OC0bMowKusauWVlIu98l9VHJeuYBHDhMZIyS/CymIiNDHR3UTzOovhIEs4I4bVthxkc4MO0EcEcKqx0d7H6hdNtaux0zthwNv3ifAYHeJPoQdvgSQAXHiMps5RJw4JkBEobTCb7lmwTogJ55qrJxA0NbJ70JHqmMy1wgNERg5g+IsSjxuTLb4rwCA1NNlKOlTFteLC7i+KxRkUMYt1953Lu2AhGhPo1bz0neuZ0Gzq0Nm1EMJnF1R7T/yABXHiEw4VV1DXapAOzk5wzVZ3bz4ke6GAceEvTRoQAkOwhrXAJ4MIjZOTZ87ljhwxyc0mMITpEArirdDQOvKVJw4KwmBTfHfWMMfkSwPvAoYJKbDbPm4brSTLyK1DKnmcUHXNuN3cwv1KCeA91NBOzJV8vMzNGhrIhPc8jptZLAO9lB/IquPBPm/nzxgPuLopHy8ivZESoHz5Ws7uLYgiBPlaCfK38ccMBFv5lC1V1njfN2yi6kgMHWDQpikMFVWTku38UkATwXvbp3hy0hr9/9QOpx8rcXRyPdTCvkjHS+u4SZwdmVX0Tn6fl8lHSMdlLsxs6WsyqtQVxQ1AKj5iZKQG8l61LyWFydBCh/l48+N5eGmRBolM0Ntk4VFjJGMl/d8kd540iflgg4YO8+dVHqfz07WR+u1Ym93Td6ZeTbW1wgA9nxYSyLiW3NwvVKT0K4EqpYKXUe0qp/UqpfUqpWa4qWH+wP7ecjPxKrjwzmt9cFk96TjlX/GM7L27+wd1F8xg/FFRy88rvaGjSjB0c4O7iGMrDiyfw6b3nsjB+CNX1TYT5e/H6t5l8d8QzOtiMwtaFHLjTovhIvs+r4KCb0yg9bYH/FfhMax0LTAH29bxI/YPNplnxSRoB3hYWT4piQVwk9104lpr6Jn6/bj9f7M9zdxE9wsfJx9l2sJDZo8M4Z0y4u4tjSDfMimHxpEjW/ORcgv2svLUj091FMpSu5sABFsZHAvCZmxcY63YAV0oFAucBrwJoreu11qUuKpeh5JXXMv9Pm08Kym/uzOTbQ8U8eskEwh17Gf5s/jjW/ORcxg8J4NEPUyWdgn36/PjIQN68bSaRQT7uLo4hjRsSwN+vO5PIIB/mTxjChn2eteCSpzsxCqXzz4kK8mX6iGD+tOEAF/95s9t+3j1pgY8CCoB/KaWSlFKvKKX8W5+klLpdKZWolEosKCjowcu5h9aa/PLa0z7+6IepZORX8uaOTGrqm/j2UBFPrd3HnDFhLD9r+Enne1lM/Gz+WHLKatlxaGB/1bXZNMlZpbJ4lQstnhRFRW0j2w963trVnsrWPBywCxEceGJpHJdNHcaBvEq2HSykoKKuz4cW9iSAW4DpwD+01tOAKuCXrU/SWr+ktU7QWidERET04OXcY21KLmc/tYktB9r+47PjcDEb9+URFeTDloxClj6/latf+hYN/P7yyW2urzB3/GD8vGR950OFlVTUNsr0eReaPSaMAB+LR4yQMIrutMABpgwP5vdXTCbAx8KKT9I567cb2bQv3/UFPI2eBPBsIFtrvcNx/z3sAb1f+Tj5GFrDwx+ksHLbYVZuO0x2yYmJE2v25uBrNfP0lZOpb7RxML+SFUsn8tl95zG8nY15faxmLogdzOepuTS1mOBzML+C9OPlvV4nT7G7efnYEPcWpB/xtpiZP2EI69PzOFJY5ZG7yHga3cVRKC15WUzMnzikeTPu1ON9O1S42wFca50LZCmlxjsOXQj0qzFMlXWNfHWggLNHhlJaXc+K1emsWJ3OtS/voLq+kSab5rO0XObFRjBndDijwv25fuYIbpozsnmmXHuWTRlKUVU9b+442nzsnjeTuO0/iR4xw6svbD9YSIiflVHhp2TeRA8smhRFWU0Dy57fyg2v7ZRJPh2wObqiuhG/AbhyejQ+VnsozSvv20WuLD18/r3AG0opL+AQcHPPi+Ref95woHloUHFVPfWNNu5fMJ74oUHUNjSxJ7uUm/71Hde+vINgPysFFXUsio/CZFJs+Pn5nf4aNn/iEM4dG85T6/aTeLSEhXGR7M+tAGBvdhlT+nlaoa6xiY378rlkkv1nJ1zn3LHh+HuZmzfhfScxi8zian4+fxwBPlY3l87zOJtL3WmBA8weE07qigVc8eI3fb6sQY8CuNY6GUhwTVHc73BhFX/dlEFUkA/+3vYfzYWxgzlzRAgmk8LXy8zc8YN5cOF4Pth9jMq6Rs4eGcqFEwYDYO5CIFJK8fsrJvOzt5P5Yl8+n+w53nyNtak5/T6Ab80opLKukUWTIt1dlH7Hx2rmrnljKK9t4P1dx/j1p+loDWMGD+K6s89wd/E8TneGEbZmMZsYHuJLSh/Ptu5pC7xfWefoVHzvx7MZFtz+zuh3zR3DXXPH9Pj1hgX78s4ds9h2sJDrXtnBtBHBBPhY+dfWI3y4+xiBvlaeu3oaE4f2vx1q1qbkEuhjYfZoGfvdG+6eZ/98VtU18vq3mZhNinUpuc0B/NWthzmYX8FTl092ZzE9gm4O4D37Jjgi1I/PUnNpbLJhMffNJHcJ4C2sS8ll6vDg0wbv3jBnTDh/uGISoyMG4WUx8dbOLECzIT2P+9/dw8f3zMFqNqG1pq7RZvgFn+obbWxIz+WiiUNk951edsd5o4kK8qW8toFXvj5MSVU9Qb5WXtryA0WV9Ty+JA5fL2N/nnqqu6NQWhse6kejTZNTVtvuAAZXk98eh6zialKOlbHYTV/pl581goSYUCZHB/PU5ZN46vLJ/OaySaTnlPPPzT+gteaeN5O46E+bDb8LyzeHiiivbWRxfJS7i9LvDQ/14+55Y1g6eShNNs1b32WSlFVCXnkdjTbd56MmPFHzYlZdHAfeWvMmGyV9lweXAO7gTJ8s8qCgsjA+kksmR/HcpoP8bu0+1qTkkF1Sw0Pv7eXL/flordmdWUJZtbEC+rqUHAZ5WzhnrKRP+krc0EAunjiEv27M4G9fHMTiaG4mZXrOBr3u4syB97gF7oZNNiSAO6xNyWXSsKA+++rTWU8uiyPE38rLXx9mRkwo98wbw2dpudy88jseen8vV/xjO8+s3+/uYnbJlgMFnD8uwvCpICNRSvGby+IJ8LHy1fcFzJ84hOGhvh61Qa+7NM/D7GEOPCrYB2+LibQ+nMshOXDgeGkNyVmlPLhwfMcn97HwQd58ef9cCivqGRrsg8Vs4tqzR/DLD1J4JzEbgM9Sc3lyWXyXRsG4S0VtA8fLarl+WP/rmPV0gwN92PzAXIoq64kM8uH+d/ew43ARWuseBy8j0y4YhQJgNZuYOz6Cz9NyWbE0rk+Gx0oLHNh2sBCAiyYMcXNJ2ubnZWFEmF9zz/bQYF+eunwSM2JCuWHWGRRW1pNokCVEnWPsZelY9/D3tn+WvCwm5sVGkFdex9vfZbm7WG7VlS3VOrJ4UhR55XUkZfVNakoCOJCUVUqAj8VQO8IMC/blnTtn8dDCWLwtJu5+czcrPknz+Fmczm2oxgw2zs+6v7p0yjBmjgrlt2v2kVNW4+7iuI2rcuAAF8QOxsts6rPNHiSAA0mZpUwdHmzIGYH+3hZ+tWQi44YEsHL7ET5OPu7uIrWrscm+VoyXxT7pQbiXyaT4wxWTabDZeOSDlOY//lrrk9bocWrrWH/gqlEoAAE+ViYODWRfbt/kwQd8AK+qa+T73HJDL6j0/2aewX9vPZvpI4JZsTqNgoq+XY+hM44WVTFpxXre35XNqHD/PpvoIE7vjDB/HlgQy5ffF/BR8jG01tz2n11c9eJ26htPrFdfXtvABX/8ij9v6H+bczfnwF30kRwR6kdWcd98oxnwv0V7s8uwaQy/JrXZpHj6yilU1zfx0Pt72f5DIVprMouqWZ+Wy/q0XA4XVvVpmYoq61iflsv3uRWs3nOcmoYmiqrqGTtE8t+e5KbZMUwfEcyTq9N55vPv2bgvj92ZpSdt/ffU2n0cLarmqzaWVT6QV2Ho1rluboG7xohQP46V1tDYBxu2DPhRKO/uysJiUv1iTeoxgwfxi/njeGrdfr7Yn891Z4/gw6RjVDt2Kve2mFh337mM6qNc/+OfpLFmbw4mBREB3owM9yenrIYp0UF98vqic5x//Jf+bSt//+oHZo8OI8TPixe+PMgt54xkT1Ypb+3MItjPSvrxMmobmpqHgH6elssd/93FLXNG8vjSiW6uSfecyIG7JoQPD/WlqY9mZA7oFvjmAwV8sPsYd54/mmA/L3cXxyXuOH80m35xPoviI3ljRyYKeOu2mbx35yy8LSYeen9vn3R0aq357nAxc8dHEBnoQ155HdedPYJtD13ATbNjev31RdeMGTyIrx+ax6f3nsO/b5nBTXNiqGu08eme4/zyg72MCvfnyWVxNDRpPkw6xrqUHEqr6/nVR6lYzYp/bT/MboNOCurpaoStOYN2X0zoGdAB/M0dR4kM9OHeC3u+MJUnGR0xiN9cFs+kYUH85n/imTU6jISYUB5YGMt3R0pIyirt9TLklNWSX1HH3HERPH3lFEaG+7Nk8lDCBnlL/ttDhQ/yJn5YEFaziTNHhBAR4M3jn6SRXVLDH66czMxRYYB9c5Mfv7GbW/+dSHFVPW/870xC/bx49evDbq5B97hiNcKWnDMyMyWA9x77NPRSZo4KxdvS/2YEhg3yZvW95/A/06Kbj106dShWs+Kd77L4+dvJ7OnFQJ7suPa0ESGcMzacL++fK5sWG4jJpFgYF0l9o40bZ8VwVkwoQwJ9GBbsi0nBkEBvdh0t4cfnj2bGyFAWTYrki/351NQbbzPl5hy4iwJ4VJAPFpPqkzVRBmwO/HhZLQUVdYYefdJVgT5Wzh0bwSrHxI3dmSWs+cm5zWufg32jYaDLQyqds/lsNvsGVbuPluBlMTEhSmZcGtWNs2Oob7TxwIITM5R/cuEY6ps0U6ODeX93dvO318XxUbz+bSZffp/PgrhITKrnU9P7inZxDtxiNjE02JfMPhiJMmADeHLzfozBbi1HX1sUb28pnTs2nK8zCol74nMunTqUvyyfylffF3DXG7tpaLLxn1tmMHtM5xabeue7LJ7/8iBPXT6Jn76d3DyM8cwzQmS5WAMbM3gQf7jy5PXCl581ovn2pBad0TNGhhLq78Vdb+wGYGS4P+/dOYuwQd59U9gesLl4FArAGWF+pB0r6/W1wQdsAE/KLMHbYiI2cmC1EJdNtS8retm0YXydUci6lBw+SDrGuCEB/Hv7EYaF+JJfXst7u7NPCuA2m+ZocTUjW+1fmVVczYrVaVTXN3H9qzsY5G3hZxeNQymYN35wX1dPuInFbOL5a6aReLSExiYb/9j8A0+uTue5a6a5u2gdcuVUeqflZw3nnjeTeHXrYe44f7TLrtvagAzgNfVNfJaWy5ThwQOuhehtMXP1DHsrav7EIVwQO5ijxdU88/n3WEyK1246i5Xbj/B5Wi51jU3N/QNvJ2bx8Acp/PuWGZw/LqL5en/dlAHAj+eO5h9f/cBjSybyo4ThfV8x4Xazx4Q3/9FXSvHXTRncft4o4od59rBRV3diAlwyKYqPJhzjuU0Z/O+5o3ptobmBFb0cnl3/PdklNfx8/jh3F8XtzCbFG/97Nm/dNpMvfjGX+GFBLJ4USUVtI9sOFrI/t5zvjhSz2rFn58Pv76WitoEtBwo4mF/B+rRcFsZH8tDCWLY+NE+CtwDsk4PMJsXalBx3F6VDrtpSrSWlFBfHRVJV39SrwwkHXAu8vLaB/35zlB8lRDcPixrofKxmZo0+8bOYMyac8EFe/GnDAXJKa6moa6Sxycbc8RFsPmDPk287WIiP1Ux1fVPzzjrRIZ61lrpwnxB/L2aPDmNtSg4PLBjv0R2aGtcsZNWac8G2jPxKYlqlHl1lwLTACyrq+NVHKbz+7VHqm2wsP0taiu3xtph5YmkcqcfKKatpwNtiwqbhwQWx3DJnJF9nFBLka6W6vkl21hHtWhQfxZGiaq57ZQc3vLaTz9PsK/R9n1vBEx+nUl3f6OYS2tl6aT30EwG8wuXXdhoQLXCtNY9+mML69DzAPoZ12vCBM3ywO5ZMjmJ/bjlnhPkT4ufFpn15TIgK4P6Lx1Na3cDVM4aTeKQEq1nJzjqiTZdMimJdag4VtY3kl1fx01XJrL73HO59azcH8iqxmE08tsT90+9r6m349EJfWKCPlchAHw7mVbr82k4DIoCvSclhfXoeCWeEkHi0hEXxUYZcOrYvKaV4YEFs8/35E+2bXfh6mfnjj6YAcFZMqFvKJowhyM/Kf289G7DvenXxn7ew4C9baLJpEs4I4bVth1k8KYozz3BvY6q0ur7XltIYO2RQ8xr4vaFfp1Cq6xvZnVnCEx+nMTk6iLdun8mvL43jjvNHubtoQgwoQ4N9WXnzWdwyJ4Y/L5/CyltmMDTIlwff20P68XK3rmZYWtNAiL+1V649ZvAgDuZXNk+Qc7V+3QK//909rE3JxWpWvHHl2VjNJm6YFePuYgkxICXEhJLQ4lvb7y6fxI2v7WTxc1+zeFIkL1w73S2dnSXV9QT79lILfHAANQ1NZJVUc0aY6zsye9wCV0qZlVJJSqlPXVGg9jiHrrW1kl5RZR2bW61TrLXm20PFnD8ugnX3nTfgJuwI4enOHxfBp/eewy1zRrI2JZc1KTmU1TSwNaOwT8tRWt1AsF/vtMAnO2arJvfSukOuSKHcB+xzwXXapbXmZ2/v4YbXdrKm1bhSm01zz5tJ3PjaTrJbLB6TWVxNcVU9C+IiZf9FITxU/LAgHlkcy+ToIB7/OI07/pvI9a/uaB6x0hdKq+sJ6aUceGxkAD5WE0mOpTtcrUcBXCkVDVwCvOKa4rRt9d4cNu7LI8DbwhMfp1FaXc9zmzK4+83d3PivnXxzqAiAz1JPvOlJA3StEyGMxmI28fSVk6mobeDbQ8UEeFt4+IMUfvZ2Mtkl1byTmMUX+/Paff7Hycf4MCm7W69ts2nKanqvBW4xm5gcHdxrSzj3tAX+F+BBoN29g5RStyulEpVSiQUFp27H1BlHCquYPiKY/9w6g6Kqel7cfIg/bTjAriMlHC+t4ZoZI5gQFci6FgF8d2YJfl5mxsn2XUJ4vNjIQH59aTzLE4az6o6ZDA/14+PkY7y85RBPfJzG/326r8306YG8Cu5/dw8rPkmnoRtbmJXXNmDT9OqGLtNGBDfvZORq3e7EVEotAfK11ruUUnPbO09r/RLwEkBCQkK3umJ/cuFYfjx3NBaTYlS4Py9tse/V9+6ds5p3v3j+iwyeXX+As3+3EYCS6gbOHBHSa2sQCCFc65oZI7jGsU7Px3fP4YbXdvLfb49i03C4sIrv8ypO6stqsmkeeG8vNg1lNQ1880MR57VYp6czSqsbAAjppRY4wLThITQ0HSLteLnLh0z2pAU+B1imlDoCrAIuUEq97pJStcFqNqGUYtGkSGza3jnQcr+5q2eM4IZZZzBv/GDmjR/M5dOGcd9FY3urOEKIXrY43v67HuRrxaTgvcRsqursszdLqur5+5cH2ZNVyu8vn8QgbwsfJh2jtLq+S69R4ji/t1IoANPPCOby6cPw7YUJb91ugWutHwYeBnC0wO/XWl/vmmK1b/GkKF748gcWT4o66Xj4IG9+fWl8b7+8EKKPXBwXya8+SmXJ5CgOFVTxytbDfJB0jIcXxfLIhyk0NGnmTxzClWdGs+1gIR8mHWNtSg5fPziPwYGd2/3J2QLvzRTK4AAf/vSjqb1ybcONA48bGsRbt81k+hnB7i6KEKIXhfp78d6PZzMyzJ/y2ga2HSzkydXpPPCefZPl+y4ay/yJQ1BK8eglE5kyPJgnV6fzWVpu83yPzKJqEo8WM25IQJvL2pbW2FvgvTUKpbe5JIBrrb8CvnLFtTqj5cp5Qoj+a+rwYMA+Lf/qGSNotGl+syadp6+cfNKkoIgAb26eM5I3dmSyNiWHG2bFUFRZx2V/30ZxVT1Bvla+e/SiU9b/L6lytMB9ey+F0psM1wIXQgxc1888gyvPjG53AbXF8ZE8/+VBHv5gL+k5FVTWNnL/xeN4dv0B1qQcJ/14OZV1TZhNcOOsGEqr61EKAiWACyFE7zvd6peXT4/mo+TjbNyXj0nB40snclVCNC9uPsQD7+5FY0/NlNc0sP1gEQkxIQT5Wg07Wk0CuBCi34gJ92fLg/NOOX7RhMF8lHychxfFcsf5o9l2sJDrXtlBZnE10SG+biipa0gAF0L0e3fOHU1UsC+3njMSsO869ZvL4tn+QyHnje3a2HFPotqa3dRbEhISdGJiYp+9nhBC9AdKqV1a64TWx/v1euBCCNGfSQAXQgiDkgAuhBAGJQFcCCEMSgK4EEIYlARwIYQwKAngQghhUBLAhRDCoPp0Io9SqgA42s2nhwN9u121e0g9+xepZ//hzjqeobU+ZcponwbwnlBKJbY1E6m/kXr2L1LP/sMT6ygpFCGEMCgJ4EIIYVBGCuAvubsAfUTq2b9IPfsPj6ujYXLgQgghTmakFrgQQogWJIALIYRRaa1d/g94DcgHUlsdnwW8DIQBXwKVwPNtPP9h4Drg50A6sBfYhH0spPOcG4EMx78bWxwfCexwHH8b8HIcV8BzwEHH9ab3sI4+wE5gD5AGPOkJ9Wzx+FlAE3ClC97PI0AKkAwkekI9gSBgdYuf/809rON4R/2c/8qBn/ZhPe9xfDY1EN7i+HWO6+wFtgNTXPB+3gekOn5uP+3j97PNejoem+v42acBm7tRr1PiDnCV43o2IKGN5+wCvIDfAllAZRvnRAHrganAN47r7QWWd+Jz2u77BywEvnf8PH7Zrfeypx+Gdn6Q5wHTOTWAPwlcAfgD5wB3tvMB+RKIAOYBfo5jPwbedtwOBQ45/g9x3A5xPPYOcLXj9ovAjx23FwPrsAfymcCOHtZRAYMct62ON2+mu+vpuG8GvgDW4roAHt7GcXe+n48Af3DcjgCKafVHrAf1NQO5OAJSH9VzGhDT+mcNzG5xziIXfG7jsQdvP+xbKm4ExnpAPYOx/zEY4bg/uBt1OyXuABOw/3H+ilYB3FGOTxy3Z2IP1G0F8JuBXwDjWvyshgI5QHAHn9M23z/HZ+wHYBT2PyB7gIldrXOvpFC01luw/0K1diGwUWtdpbXeCtS2PkEpFYj9F7FAa/2l1rra8dC3QLTj9gJgg9a6WGtdAmwAFiqlFHAB8J7jvH8DlzluXwr8R9t9CwQrpaJ6UEetta503LU6/jl7hN1ZT4B7gfext0Z6kzvrqYEAxzmDsH/eGl1Yrx+01kdb3O+1egJorZO01kdaX1drvd1xbutrddcE4FutdbXWuhHYDPyPu+sJXAt8oLXOdJzX5c9uW3FHa71Pa/19O09ZBHzmOO9brXVOO+ctBNZprQ9orTMc5x/H/vsVcbrP6WnevxnAQa31Ia11PbAKe4zqkj7LgSulwoEGrXVZB6dehP3rWGu3Ym9BAwzD/nXHKdtxLAwodXwwWx4/3XO6TSllVkolY38jN2itd7i7nkqpYdh/IV/seo3apYH1SqldSqnbHa/j7vfzeezB6Dj29M59Wmtbl2rVvquBt6DP6tlZLa/VXanAeUqpMKWUH/ZvpsM9oJ7jgBCl1FeOz9kNHVXEBRbiCODtUUqZgfFa6/RWx2dgbzn/wOk/py258rMA9O2u9BdjzyN1ZCHwr5YHlFLXAwnA+c5DbTxPn+b46Z7TbVrrJmCqUioY+FApFQ9Mxr31/AvwkNa6yd4wcIk5WuvjSqnBwAal1H7sLQl31nMB9nzpBcBoR7m+1lqXd6JM7VJKeQHLsOd5oW8+t50p1zzsAeCczpzfHq31PqXUH7C3iiuxf3VvxP31tABnYv8W4At8o5T6Vmt9oBNl6jLH+xyttT7UwalnY0+PtnxuFPBf7Ll9m2r7F023ek7r988l8agvR6E0f13pwAzsnYMAKKUuAh4Flmmt6xyHs4HhLZ4Tjb0lVog9NWJpdfx0z+kxrXUp9hzbQtxfzwRglVLqCHAl8Hel1GVdrVNLjq+Lzq+1HzrK7u563oz9K7fWWh8EDgOxXa/dKRYBu7XWeS3u93Y9T0spNRl4BbhUa13UibKcltb6Va31dK31edhTDhm4v57ZwGeO9E0hsAWY0pn6dNO5wNZOnHfSz8WRQloD/MqRioXTf07be/9cE4/aS4739B/2DoJUx22F/S+9anXOTbToJAHigFUt7k/D/hVlbKvnhWL/hQ1x/DsMhDoee5eTOxPucty+hJM7MXf2sH4RnOjA8AW+Bpa6u56tnr+SHnZiYu/QCmhxezv2D7W7389/ACsct4cAx2ijo7Ub9V2FY0RLX35uW5xzhJM790ZgH6Uw24W/m4NbXHu/oyzurucE7KkZC/YO1lQgvht1i6HV4AnH8a9o0YkJPAMsbOO8ylb3twOBjttejjL+tI3ntfc5bfP9c9TzEPbRK85OzLgu19dVH4pWhXsLew9tA/a/NA8BK9t4A4uxf43LBiYC9wM3tThnI5DHiaFdn7R47BbHD+YgLYaQYe/V3ek4/i7g3eKX8QXHBy6FNoYUdbGOk4Ek7MODUoHHsbd+3VrPVq+9kp4H8FGOD5dzuN6jnlBP7KMA1jvey1Tgehd8bv2AIiDIcb8v6/kTx/UasbfEXnEcfwUoaXGtRBfU82vsIz72YE9ZuL2ejscecJQrlTaCZCfq1Tru3Iq9PygbqHOU9XPHud8Bvi2e+7TjPJvj/xXYG2lftDjnese1k1v8m9rB57Td9w97/8MB7DHp0e68l30ylV4p9SvsPa6rOjhvA3CDbr832KNJPU85T+ppAAOlnk5KqWjgZa31og7Oux57nvz3fVOyrpO1UIQQwqBkKr0QQhiUBHAhhDAoCeBCCGFQEsCFEMKgJICLfkkp1aSUSlZKpSml9iilfq6UMrU652Ol1DeO2wsc5ycrpSqVUt87bv9HKTVXKVXW4vFkxwQWIdxKRqGIfkkpVam1HuS4PRh4E9imtX7CcSwY+xjySmCx1vpwi+d+BdyvtU503J/ruL+kD6sgRIekBS76PW1fAuB24J4W61ZcgX098VXYF68SwnAkgIsBQdsXLTIBgx2HrsE+c+8tx+2OnNsqhTK6l4oqRKf15WqEQribAlBKDQHGAFu11lop1aiUitdap57muV9LCkV4GmmBiwFBKTUK+xZz+cByHIssOVZtjEHSKMKAJICLfk8pFYF9hbjntb3X/hrsK9HFaK1jsK9DLQFcGI6kUER/5evYLcmKfeW7/wJ/UkrFYF/i07mWM1rrw0qpcqXU2VrrHW1dDEcOvMX932it32vnXCH6hAwjFEIIg5IUihBCGJQEcCGEMCgJ4EIIYVASwIUQwqAkgAshhEFJABdCCIOSAC6EEAb1/wG9a6/TdwT2wQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# line plot of dataset\n",
    "series.plot()\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "280419a5",
   "metadata": {},
   "source": [
    "## Split the Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "956da704",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset 252, Validation 12\n"
     ]
    }
   ],
   "source": [
    "# split the dataset\n",
    "split_point = len(series) - 12\n",
    "dataset, validation = series[0:split_point], series[split_point:]\n",
    "print('Dataset %d, Validation %d' % (len(dataset), len(validation)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d23dd458",
   "metadata": {},
   "outputs": [],
   "source": [
    "dataset.to_csv('dataset.csv', index=False)\n",
    "validation.to_csv('validation.csv', index=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "062abc12",
   "metadata": {},
   "source": [
    "## Develop the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e1072a2b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# create a differenced series\n",
    "def difference(dataset, interval=1):\n",
    "    diff = list()\n",
    "    for i in range(interval, len(dataset)):\n",
    "        value = dataset[i] - dataset[i - interval]\n",
    "        diff.append(value)\n",
    "    return numpy.array(diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a84d0691",
   "metadata": {},
   "outputs": [],
   "source": [
    "# invert differenced value\n",
    "def inverse_difference(history, yhat, interval=1):\n",
    "    return yhat + history[-interval]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0a95fb00",
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.tsa.arima.model import ARIMA\n",
    "import numpy\n",
    " \n",
    "# create a differenced series\n",
    "def difference(dataset, interval=1):\n",
    "    diff = list()\n",
    "    for i in range(interval, len(dataset)):\n",
    "        value = dataset[i] - dataset[i - interval]\n",
    "        diff.append(value)\n",
    "    return numpy.array(diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "18ba1087",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                               SARIMAX Results                                \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   No. Observations:                  240\n",
      "Model:                 ARIMA(0, 1, 0)   Log Likelihood                -271.408\n",
      "Date:                Sun, 20 Mar 2022   AIC                            544.816\n",
      "Time:                        23:27:39   BIC                            548.292\n",
      "Sample:                             0   HQIC                           546.217\n",
      "                                - 240                                         \n",
      "Covariance Type:                  opg                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "sigma2         0.5674      0.006     97.020      0.000       0.556       0.579\n",
      "===================================================================================\n",
      "Ljung-Box (L1) (Q):                   0.08   Jarque-Bera (JB):            243840.50\n",
      "Prob(Q):                              0.78   Prob(JB):                         0.00\n",
      "Heteroskedasticity (H):              50.19   Skew:                            11.08\n",
      "Prob(H) (two-sided):                  0.00   Kurtosis:                       157.90\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n"
     ]
    }
   ],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "# load dataset\n",
    "series1 = read_csv('dataset.csv', header=0)\n",
    "# seasonal difference\n",
    "X = series1.values\n",
    "months_in_year = 12\n",
    "differenced = difference(X, months_in_year)\n",
    "# fit model\n",
    "model = ARIMA(differenced, order=(0,1,0))\n",
    "model_fit = model.fit()\n",
    "# print summary of fit model\n",
    "print(model_fit.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55fe8b76",
   "metadata": {},
   "source": [
    "## One-Step-Out-of-Sample Forecast"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e021c909",
   "metadata": {},
   "source": [
    "### Forecast Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b23aeea1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# one-step out-of sample forecast\n",
    "forecast = model_fit.forecast()[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "aca56cbd",
   "metadata": {},
   "outputs": [],
   "source": [
    "# invert the differenced forecast to something usable\n",
    "forecast = inverse_difference(X, forecast, months_in_year)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4ba2b37c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Forecast: 6.600000\n"
     ]
    }
   ],
   "source": [
    "print('Forecast: %f' % forecast)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "929246f9",
   "metadata": {},
   "source": [
    "### Predict Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b3809005",
   "metadata": {},
   "outputs": [],
   "source": [
    "# one-step out of sample forecast\n",
    "start_index = len(differenced)\n",
    "end_index = len(differenced)\n",
    "forecast = model_fit.predict(start=start_index, end=end_index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f4a70035",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Forecast: 6.600000\n"
     ]
    }
   ],
   "source": [
    "# invert the differenced forecast to something usable\n",
    "forecast = inverse_difference(X, forecast, months_in_year)\n",
    "print('Forecast: %f' % forecast)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20aacc0e",
   "metadata": {},
   "source": [
    "## Multi-Step Out-of-Sample Forecast"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "018631e9",
   "metadata": {},
   "source": [
    "### Forecast Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "6217fc72",
   "metadata": {},
   "outputs": [],
   "source": [
    "# multi-step out-of-sample forecast\n",
    "forecast = model_fit.forecast(steps=12)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "28c212dc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Month 1: 6.600000\n",
      "Month 2: 6.600000\n",
      "Month 3: 7.500000\n",
      "Month 4: 17.800000\n",
      "Month 5: 16.300000\n",
      "Month 6: 14.100000\n",
      "Month 7: 13.300000\n",
      "Month 8: 11.500000\n",
      "Month 9: 11.000000\n",
      "Month 10: 10.000000\n",
      "Month 11: 9.800000\n",
      "Month 12: 9.800000\n"
     ]
    }
   ],
   "source": [
    "from pandas import read_csv\n",
    "from statsmodels.tsa.arima.model import ARIMA\n",
    "import numpy\n",
    " \n",
    "# create a differenced series\n",
    "def difference(dataset, interval=1):\n",
    "\tdiff = list()\n",
    "\tfor i in range(interval, len(dataset)):\n",
    "\t\tvalue = dataset[i] - dataset[i - interval]\n",
    "\t\tdiff.append(value)\n",
    "\treturn numpy.array(diff)\n",
    " \n",
    "# invert differenced value\n",
    "def inverse_difference(history, yhat, interval=1):\n",
    "\treturn yhat + history[-interval]\n",
    " \n",
    "# load dataset\n",
    "series = read_csv('dataset.csv', header=0)\n",
    "# seasonal difference\n",
    "X = series.values\n",
    "months_in_year = 12\n",
    "differenced = difference(X, months_in_year)\n",
    "# fit model\n",
    "model = ARIMA(differenced, order=(0,1,0))\n",
    "model_fit = model.fit()\n",
    "# multi-step out-of-sample forecast\n",
    "forecast = model_fit.forecast(steps=12)\n",
    "# invert the differenced forecast to something usable\n",
    "history = [x for x in X]\n",
    "month = 1\n",
    "for yhat in forecast:\n",
    "\tinverted = inverse_difference(history, yhat, months_in_year)\n",
    "\tprint('Month %d: %f' % (month, inverted))\n",
    "\thistory.append(inverted)\n",
    "\tmonth += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a65c8f2",
   "metadata": {},
   "source": [
    "### Predict Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bf7ece89",
   "metadata": {},
   "outputs": [],
   "source": [
    "# multi-step out-of-sample forecast\n",
    "start_index = len(differenced)\n",
    "end_index = start_index + 11\n",
    "forecast = model_fit.predict(start=start_index, end=end_index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "9508566e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Month 1: 6.600000\n",
      "Month 2: 6.600000\n",
      "Month 3: 7.500000\n",
      "Month 4: 17.800000\n",
      "Month 5: 16.300000\n",
      "Month 6: 14.100000\n",
      "Month 7: 13.300000\n",
      "Month 8: 11.500000\n",
      "Month 9: 11.000000\n",
      "Month 10: 10.000000\n",
      "Month 11: 9.800000\n",
      "Month 12: 9.800000\n"
     ]
    }
   ],
   "source": [
    "import csv \n",
    "# Predict Function\n",
    "from pandas import read_csv\n",
    "from statsmodels.tsa.arima.model import ARIMA\n",
    "import numpy\n",
    " \n",
    "# create a differenced series\n",
    "def difference(dataset, interval=1):\n",
    "\tdiff = list()\n",
    "\tfor i in range(interval, len(dataset)):\n",
    "\t\tvalue = dataset[i] - dataset[i - interval]\n",
    "\t\tdiff.append(value)\n",
    "\treturn numpy.array(diff)\n",
    " \n",
    "# invert differenced value\n",
    "def inverse_difference(history, yhat, interval=1):\n",
    "\treturn yhat + history[-interval]\n",
    " \n",
    "# load dataset\n",
    "series = read_csv('dataset.csv', header=0)\n",
    "# seasonal difference\n",
    "X = series.values\n",
    "months_in_year = 12\n",
    "differenced = difference(X, months_in_year)\n",
    "# fit model\n",
    "model = ARIMA(differenced, order=(0,1,0))\n",
    "model_fit = model.fit()\n",
    "# multi-step out-of-sample forecast\n",
    "start_index = len(differenced)\n",
    "end_index = start_index + 11\n",
    "forecast = model_fit.predict(start=start_index, end=end_index)\n",
    "# invert the differenced forecast to something usable\n",
    "history = [x for x in X]\n",
    "month = 1\n",
    "for yhat in forecast:\n",
    "    inverted = inverse_difference(history, yhat, months_in_year)\n",
    "    print('Month %d: %f' % (month, inverted))\n",
    "    history.append(inverted)\n",
    "    month += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "7dd84619",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'Month 1': '6.6', 'Month 2': '6.6', 'Month 3': '7.5', 'Month 4': '17.8', 'Month 5': '16.3', 'Month 6': '14.1', 'Month 7': '13.3', 'Month 8': '11.5', 'Month 9': '11.0', 'Month 10': '10.0', 'Month 11': '9.8', 'Month 12': '9.8'}\n"
     ]
    }
   ],
   "source": [
    "dicts = {}\n",
    "\n",
    "keys = ['Month 1', 'Month 2', 'Month 3', 'Month 4', 'Month 5', 'Month 6', 'Month 7', 'Month 8', 'Month 9', 'Month 10', \n",
    "       'Month 11', 'Month 12']\n",
    "values = [\"6.6\", \"6.6\", \"7.5\", \"17.8\", \"16.3\", \"14.1\", \"13.3\", \"11.5\", \"11.0\", \"10.0\", \"9.8\", \"9.8\"]\n",
    "\n",
    "for i in range(len(keys)):\n",
    "    dicts[keys[i]] = values[i]\n",
    "print(dicts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "a070f093",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame.from_dict(dicts, orient='index')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "9f19c25a",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>0</th>\n",
       "    </tr>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Month 1</th>\n",
       "      <td>6.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month 2</th>\n",
       "      <td>6.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month 3</th>\n",
       "      <td>7.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month 4</th>\n",
       "      <td>17.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month 5</th>\n",
       "      <td>16.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            0\n",
       "Month 1   6.6\n",
       "Month 2   6.6\n",
       "Month 3   7.5\n",
       "Month 4  17.8\n",
       "Month 5  16.3"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "45fb9127",
   "metadata": {},
   "outputs": [],
   "source": [
    "df.index.rename('Months in 2022', inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "25e1bb9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Months in 2022</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Month 1</th>\n",
       "      <td>6.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month 2</th>\n",
       "      <td>6.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month 3</th>\n",
       "      <td>7.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month 4</th>\n",
       "      <td>17.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month 5</th>\n",
       "      <td>16.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   0\n",
       "Months in 2022      \n",
       "Month 1          6.6\n",
       "Month 2          6.6\n",
       "Month 3          7.5\n",
       "Month 4         17.8\n",
       "Month 5         16.3"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "7b505165",
   "metadata": {},
   "outputs": [],
   "source": [
    "df.rename(columns={ df.columns[0]: \"Prediction Rate\" }, inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "55fbace5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Prediction Rate</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Months in 2022</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Month 1</th>\n",
       "      <td>6.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month 2</th>\n",
       "      <td>6.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month 3</th>\n",
       "      <td>7.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month 4</th>\n",
       "      <td>17.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month 5</th>\n",
       "      <td>16.3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Prediction Rate\n",
       "Months in 2022                \n",
       "Month 1                    6.6\n",
       "Month 2                    6.6\n",
       "Month 3                    7.5\n",
       "Month 4                   17.8\n",
       "Month 5                   16.3"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "df0d0dfa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Prediction Rate</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Months in 2022</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Month 8</th>\n",
       "      <td>11.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month 9</th>\n",
       "      <td>11.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month 10</th>\n",
       "      <td>10.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month 11</th>\n",
       "      <td>9.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month 12</th>\n",
       "      <td>9.8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Prediction Rate\n",
       "Months in 2022                \n",
       "Month 8                   11.5\n",
       "Month 9                   11.0\n",
       "Month 10                  10.0\n",
       "Month 11                   9.8\n",
       "Month 12                   9.8"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "11d9f5ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "df.to_csv('Arima_Test_1_Results.csv', sep='\\t', index=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8843fac6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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