lab07/TS-Exp6A.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "98f07c0e",
   "metadata": {},
   "source": [
    "# 6A. Check for the Autocorrelation Function and Partial Autocorrelation Function of the data"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "51802afd",
   "metadata": {},
   "source": [
    "**Aim**: Understand autocorrelation, Partial Autocorrelation Function, ARMA, and apply these techniques in projects.\n",
    "\n",
    "Autocorrelation Informally, is the similarity between observations as a function of the time lag between them.\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0aca3d9c",
   "metadata": {},
   "source": [
    "**ACF (Auto Correlation Function)**\n",
    "\n",
    "_Auto Correlation function takes into consideration of all the past observations irrespective of its effect on the future or present time period_. It calculates the correlation\n",
    "between the t and (t-k) time period. It includes all the lags or intervals between t and (t-k)\n",
    "time periods. Correlation is always calculated using the **Pearson Correlation formula**.\n",
    "\n",
    "**PACF(Partial Correlation Function)**\n",
    "\n",
    "_The PACF determines the partial correlation between time period t and t-k. It doesn’t take into consideration all the time lags between t and t-k_. For e.g. let's assume that\n",
    "today's stock price may be dependent on 3 days prior stock price but it might not take into consideration yesterday's stock price closure. Hence we consider only the time lags having a direct impact on future time period by neglecting the insignificant time lags in between the two-time slots t and t-k."
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": 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"
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"
    },
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "5ee05dcd",
   "metadata": {},
   "source": [
    "**AR (Auto-Regressive) Model**\n",
    "\n",
    "The time period at t is impacted by the observation at various slots t-1, t-2, t-3, ....., t-k.\n",
    "\n",
    "The **impact of previous time spots is decided by the coefficient factor at that particular\n",
    "period of time**. The price of a share of any particular company X may depend on all the\n",
    "previous share prices in the time series. This kind of model calculates the regression of\n",
    "past time series and calculates the present or future values in the series in know as **Auto Regression (AR) model**.\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "**MA (Moving Average) Model**\n",
    "\n",
    "The time period at t is impacted by the **unexpected external factors** at various slots t-1, t-2, t-3, ....., t-k. These unexpected impacts are **known as Errors or Residuals**. \n",
    "\n",
    "The impact of previous time spots is decided by the coefficient factor α at that particular period of time. The price of a share of any particular company X may depend on some company merger that happened overnight or maybe the company resulted in shutdown due to\n",
    "bankruptcy. **This kind of model calculates the residuals or errors of past time series and calculates the present or future values in the series in know as Moving Average (MA) model.**\n",
    "\n",
    "![image-2.png](attachment:image-2.png)\n",
    "\n",
    "**ARMA (Auto Regressive Moving Average) Model**\n",
    "\n",
    "This is a model that is combined from the AR and MA models. In this model, the impact of previous lags along with the residuals is considered for forecasting the future values of the time series. Here β represents the coefficients of the AR model and α represents the coefficients of the MA model.\n",
    "\n",
    "![image-3.png](attachment:image-3.png)\n",
    "\n",
    "_We know that in order to apply the various models we must in the beginning convert the series into Stationary Time Series. So, apply the differencing or Integrated method where the t-1 value is subtracting from t values of time series. After applying the first differencing if we are still unable to get the Stationary time series then, again apply the second-order differencing._"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd402361",
   "metadata": {},
   "source": [
    "**Aim**\n",
    "- To plot and review the partial autocorrelation function for a time series.\n",
    "- To find the difference between autocorrelation and partial autocorrelation functions for time series analysis.\n",
    "\n",
    "**Dataset – Minimum Daily Temperatures Dataset**\n",
    "\n",
    "- This dataset describes the minimum daily temperatures over 10 years (1981-1990) in the city Melbourne, Australia. The units are in degrees Celsius and there are 3,650 observations. [Source: Australian Bureau of Meteorology]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5344c9f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ibMozvF3DEn+rJo29otSdmhdcsetIle+05gv8uvzRF4o8mnwrXyzZhRs+XoKZ6/lkiVGjrubjZ6QJxVW7j3GXQ00kKm29lGdqhr49D8PftT4SUi4dXHvqMo3uLOWJU8/7yv8uqrJ8VtkQFAn4QpG7OdlpFFYra3IOSYmVdx85jVKWW7Mt4/rC3qpfcRbp5RmbmF5vY5680ilECGS7QctI+YoJ45VVFqCutznd5BMMOFlYeYnwn1uq7jTPfHE2dh+2ntycd/pABV8oci8vP2SNYjG98stmtHryF75la3zntkHshcnOcXN3ML3eu79vY3o9FhBC0PvVP9CBQ0LzUDjpUjTiNjldXIbe//nDchn/nLzK8rl28IUi94NFHgnvGq2hvhND3U15J/Dt8j3hD4Te8kM2Mu07dgYfz2OrpL0GhfEX395jZ8pXuXwyfyf2HLFumVrF7Z2ddnFr968vVq2Ec5G/PGMTygIUTw/vwEcgBwgEqKbSPMPRj6k18gk1/LfKRW/PM3yslp94SMcGTOR47Pt1AIBLupyF9FpJYY5mB49Rjl6X0Rvdqr/NLyjCCz9vxJdLduH3h/uyFi0kTs6JuD26dBJfWOThdqONm7sDn8zfyUkaZ7h5/FJNV8oWjtvRtar5x1V7uZWvxaGTVX3FKTXZbqEt5WwG8iwtWHkZWTegKNOCQv5hJ5x8FEKRuwzvRSuTl+42lL2FJfO3HQJQ1ZKK9diKnXfn/M0ldoSTBFulEbkuXW/ZigGU6nDHpemuj9yv+EORc3ZAj/1hHYa+JQ3/DXdyG21kbe4x3d9iOD2hsgA1ZLG8PmsrZm3kvzTSSfygx82+bJQeY9RVUWkDEZQwu0Ry+XF8cZ8scs6V6IfnbBVfKHI3LAOzw207b/tXZ24p/zvYAI/VuflVu9mGzm35xAy8ZHCZXbEDfnM34b1W3coIwOpchZWz1OL94+MlaPHEDEtlK6zfexynDEYHPVPs/yiibhARk51OUVIWwDsuLxXTc60s3XkE3ZrW5SyNhNuriFgXr35nf78ifIJgN7D6sqGUmn5xqDMYLdqhnwTCCGeKyzD83flonVbT1nX8CE+XnS8scrfWkX+7PNdwMgM7zyzUi0pvotdNm9jO8/CiP1ot08Oq7ETOlVfxdyBgXtEaoXxDkM73VY5XPVPFlcKi1yn5Ro2GeZi9SQqW5YTx9sovbDd2GUWEsTWAk4rhiR/XOXZtPYI7msfmOgHYkylbTg7hJhv2Ha/02c252xZPzMBz0zaGPW7pziOW2rqV7sF0MttD7+0F2+yNLqzywNerHY+b4wtFHsr/7BUDzyNicMHOu+XzhbuYyWGFM8VlOFolMYW7T++zhTlhj7l5/FJ8Y3ATFVDxsqUGZ2/UL2cl67tXklBEAqv3HHP0+r5Q5KG4+B3jm0uC+eekVfhyibuKBQjdYcZ+v5ajJMZwon9b8eVaQSvqIm+L3OrE+Jb9xqNQlq8+tFBUaYRNZkcDvpjsDMXm/dbXe09dsw9T1+zDP3o2sy2HHSUUSi8uy9FenVLiYiJiJ+IRNH98Bm7o2dRY6TaK1zqV/6qVqt8dP12CE4WhU9gVlppfmldlQ5CBcx76ZrV0LIPH7IZ70os43cR8YZF7xX3CA6N95/VZ+kkZnMapVStfLdntzIXD4IX2NXvTAWzLD21xm5GzYrLT2P4ANRv2Sf7cXAt5W4+dLsa4udvLDZvp69yJPeIFeDYrXyhynli1rF+abn1G3KrlsynvBIa9Mw8nDa7RZUWk+U69EPP84W/X4NZPl4U8ZtLS3fh6mbmXndEt+nZGtmqe+HEdXp6xGUt2Rk6sbz/gC0XufjcLzw+sYpKY0JGvztyMDftOYOlOe7PxZnfuWVXjgQDFmRLvJTM4fqYEWznGtLGDEujLKKz6Tqj8qmpOnJGMCqPLdiOBfcfOYHqYqIdOhwfwhSLniRvGmRv27eyNB8p3h240uTTKqkHuZmCzZTlH8OeWg5rd6R8fL8HgN+c6Uu6uw6eqrDbhGf2Q1QTyxMXuLwrgRf92aaaOPz/7d4z5aiUWyPGS3MAXk508lasb1r/aVfHRX8bjY9uR9fbPlwMAcrKHmU4pZlWRs4rkGBdr3v64+sNFAIA1zwyu8pvSvoa/a30FlB4j3l+AY6dLcE1mk4ryOLSy8uWHFqIfasF7N6+bzrv4WGulB6eS44mwyIPw4s7DcPDe+Wq1PFZSxtnQKgPf+Ev3t/V72W/aOFZlzTpfgpuz1eZt9AXgpemTGRYnWlfvOYaMsdOx1Ed+fl8o8jKDGddZvBGPnC62fQ2zeKjtG8JLndUsdnNhWoW/gVCxaqWyHNauFmPwobO6zeKyAD78aztKbOQQnbZmn6XzDpyQ2shfWw+aOm/93so7hnkO732hyI+cMmbVHLdp/cz/+xDOfWmOrWtEA1ZXrbB6Afhw0FQJrq7CYIvc4nV4v7unrN6H7F8221qSanc1ktmR5+eL9OcRnvxxPY45aCT6QpHzWh5258TlXMphRRULgBNuG+R+TBCgbsJcMwRVkcNa6UZf3sphJWUBZIydbqksNadshLX12gv/l/XOxfH3hSI3GsTHz0N+Kxw6af4NHwhQ2wmHrdYzK1/+sdMl+HTBTl/NZ3B3rJRPdlYu2apRZPaZn2aUa9bOI7Zb537SJ2EVOSFkPCHkICFkveq7Zwkhewkhq+V/FzspZJmPOqzXmb3pAF60sXkJACa4HPjqP79uwXPTNmKVw4GIWKJWqDwm0SoyBFX+3mpcmXgLK4Xcxq7a8JEeN2SRfwZgqMb3b1JKu8r/7KUQCUOZT4L43D5hmenhJKUUazm6SFhsyJm96YCl81hbOO7Gm/ELlfvONoNxwYM5rJEEW01+QREyxk7HvL/dW0sdjNdGbE6+GMIqckrpXACursMxapG7PRRSguKHY+ehU5iyWtoJOnnZHq4rKSJpe72f7oWrX5xSHJTbFCtddqIwtK9656FTbAoKwqoyPllUijmbza06qYLN9sUzzoydDUH3EkJuBrAcwMOUUs0wfYSQ0QBGA0DTpsai2wXDM/krD4a8ORfFZQGs2n3Ms6nFBGzhaRwu2l4RssHvPcdqvdmJfeRHrDq+/gugJYCuAPIAvK53IKV0HKU0k1KamZqaaqkws4mQvY6S/uqzhTko4B3wKuhzv9f+tHytrQcKUGQhtCorfGSQV8lK5CTqcLe8XiDBlrPR1G5hr2vxvBNn3N2IpYWT7dWSIqeUHqCUllFKAwD+B+BctmJVxrBrxYQXalmOf3ZtOYnVIfGhk0UY/OZcPPnj+vAHy/hJ8bLm8g8WulKuW0s135ljLMhWOLaHCe2rC4O2ZuQS+1zclq/GkiInhDRUfbwcgPHebIHbL2jO/JpK7I1IYOqafXjqJ2NR8Vgp0wLZZ7rc1AuRrSaP4veCYe6ftJpLOU7NV0xZbW13Ji+u/99it0UAYGz54SQAiwC0JYTkEkJuA/AqIWQdIWQtgH4AHnRSyG5N6zp5eWzc52xiVKf5cdVefLFYfwfcwROFOFhQyLRML6wIiGYL3yisApUN79ww/EEegkXTMNK+Dp4wvlDByZhIYSc7KaXXa3z9iQOy2MZqx774nXmYPPo8tsJoQCnFFy5kwTn3ZSnsQE72MOaNyYwlxl7x8tfkR08Vo26NBO7luk2Cz9aRsxghGOkrXjEm/PV0HMRKWiuzrNt7HE//5KgXKqpwoxMp+Sy9jBOWn/vjL2/iET0eWYp80tLdyBg73VLwLJbxlu/5coXm917ImuKmBeGVRm+HI6f4R8f0Al5wpZmBRX/2irVthIhS5J8uyAFgLZyt0TCdRpixTjs4jp8aRji80K0jqDo9jxeetxlYtA0jMZ7MuHBKDIbjtkJEKXIFKwozJobgFKNAP3p4YSciKwlGjl9q+noeuH37RMRNmCecQe6kxb7nyGnHrh2Kr5aync9yckTuS0V+a1YG/jmgte7vViK88Uhl5QUVcPeXK5lch8ecQji88GKMFqau2eeae+X137aYPucgg7AXrENnCEUexDOXdERqTf2VAx+ayHupwNK1ooddxeN3vcV6Em7lrqP4cRXfEAcEwJTVe5F33P0XGW8mL9sT/iAHMLqx+3RxKSYu3oWSsgAWqsIU2CFchiIzLTqlZqI9YULgi+TLWoRSimsshDe1G6PbCHat/o5n1XIkr6Rfef7njQCAvm3SuC0JLCkL4P7Jq5GRUh1/PtqPS5lOUqd6vOG8ojzDDKgJN8IuLQvg3q9WYf+JQqzecwy/bWCXwOHjeTtxd9+W+geY6NPptZxT5L6xyD+7tUelz6GsUyvbklfuPmb6HLNc+t4CW+eHs2hHvDff1vUt4YFRQrhYPKdtZJkJRilq/wljG6y8PIpKTjRnx4XadOYkP6/NCxkeeuuBk5i5YT9WywYcy1C6JwrZxWxx0jPlG0Xet21apc+hlJrPVkoxY01uaIvJCXeAh/VUOcrELAsUP7GTu/TCsfPQKczaaC0mvJobelqLRgoAS3YctjTydQK/LKl1Ui35RpEHE8pNEamKPIYANU1aUWrcji/jVodblqMZYdkSm/dLW97dVB79X/8Td3zOIL8ssd5Xrh23GCPetzfCBIBuTetgTL8QrgsDeHnUo8bVxBJeJdTDO11cioyx0/HFYndTkrGmWUoNJMXHWj5//3G28Va8QihXWv/X/3SkTB6T43qwMlRYrqKwOpFPKfDokHaY/VAfZrLwxMx9925jLYy3EXysyPUr8Kg8ecNjApMXL4zoiFeu6ASvhbwwFWvFQTn02JHvTOYao/fi5D3bXQ5oZYnezPXaWW/sytIqraat86Mdj6kF4xjpIFqTYHnHz2A0i2EpZwZ1aIAaiXFIjLNukTuBkd1vjuOGCAYaIKXUcrJjI+jWvcG3RwwhphXwXV+w2YegEMtjA0cIfhqTZet8r7h1fKvIjQxttdrof37dgt9MThS9eW0XPHtJB3x1e09T57EkRn5Swat3QlFSFsCuwxUWqRONbuehU/huRa6hGDdObeDxmh7v8dJsjP58uaNKnAVxMcR23RWWlOHTBTtx7ThrcbnfurarTQnsTTzXrhZvs2xv4ON15OGPsbLDM5g26TVxebfGtq9jF+XF1SLV+BD02akb8KUqbG5JmTOa5ZP5OwEAe46eRu3qtR0pw2uEeinlFxTht40HHN8JaffqLPz8BYWleHPWVkvnVk+IRZN61W3LIPCxRc5LkXsFo51OPdxesI3detpQbMqTNim5Ncx04zEfN5ATkuV6ZiewOt/yTdAOz0KLk6as3Cp22p3dl61XwkT4SpG/fHknfDIyE4B510qf//yB2z5b5r8wbjKxBhtM7tGKAENeaWQKToljJy/ls5d0YChJZU46nFjbbkhdq4r0X9+vrfTZ6jzJt3f1snQeK5rUq+Zq+SzxlSK/oWdTDGifbvh4dfPadfg05mw+yF4oThAfPCm3NsnY8UXfksU+H6yC0zZDTznzk8LUNftw5FSxiadAmAhp9am3a1Cr0uePb87kVv7gDun44W57E51ewgfqQRurk512223D2kk2r2ANK/5M3mo1WMSXpm/E0p1ScuZf1uWVx4tnjVeTHvCUa//xQvxz0ircOdH4iqxQBvlTw9obvk64EAlGObuRtfkVKyO9C9ukIjXZfuwTr4x5favIjTy8+Fj71cyqL1rJWqTGqGtl8rI9yBg7nWl8ESsUlZbhf/N24pqPpN2krMLnakEpcMunSzH0rbmOlaFFuHrm+X5RNvfkmdj0FUMImqfWKP/81R0Vq7LqVOefl5SnJ5BFUS/+vBGHPZIxyreK3IiFmne8EDsPObMhxCxdnv/N1vlGG/l//9wOwFx2b1aoZXzo6zXcyg1Qij+35Jdvn1+x6yjW7zUfqc/KUrSDJ4owc/1+HNQIonX0tDc6uR5llOKzW8/V/M0NS9N6mdbPNPKu/W3Dfs04RR/Lq7W8gG8VeWazuoaO6/fan7bK8crKFze3hFtBHdSpzZO/OFpW8Mj+yv8uxPB3zUeC7N8uLfxBQRSXBXDXFytw3f+qrqN+btpG09ezipXm8dWS3ahXIwE9m9eTrmFBITJtlhybuJmJ3tETV+AyBnFlnMS3ijytlju+arfUqaUVBoyETYwz1kz2HKmwWkpV+QmLwwTnD+aBgVWzP91yfgZevryT5vGsfNFWqktJPOCFjElmqVtdfwTihvkSzljJGDsdP63aCwB4Zsp6dPz3TADWXiZGXZUKB04UYc2eY8gYOx2P/7DOfIEO41tFzosaNqINssSsHmfZEd+4pquh4+74fHn5EJT1rsZhnRvi6kztjVl6ZamXYhrCgkJQ3lfFpQF8tyLX9YnX3KNnDAdHWzC2PwDvrMg1Uv0fzZXiJ01YtMtWjl0ryn/yMmlz3STGuTxZEHWK3GxH07IO3cDsmnBKqSULs0m9alUaec0k4y+zwyft+4X1Aijp3Y/eM73orXmmyrXiWlC73h75dg0WMUoxZhZ1FYw1aDFWT6j8XNXP3RUfuaGVaFWftRVZrYxwSx3aGc2CqFDkdhIq9G9nfN26l7DS5G45PwMTbj0XO18Zhhb1a4Q/QQO7PtOc7GGmJx317rXA5IYcK7KXBSkWq1bi/QNacw0g9fCgNiF/d0plNaqjvwmH58tDq66v69Gkynfq0Y2XY+dEhSLv9crvzK7Fa7ekmeBYepiV9dlLO5bHclGf6ra7QEHvfuxOSI+SNwURSLF1AKCBwTkYltEfedbzfQNUI01vPF5DL1KtKrLSJ1vUrzrqy76yc5XvfpR98gBwSmUY/LU133SZTuJrRW5m04LC4h1HHJCEPerUdkaVCkuUiaerujf2Sj/XtdgCNvMj3JqVAQC4pkcT/DQmC7Mf6o05DxtLdBCsyK2+5gkBnrjYfHtmCdH5m1v5RlwrQa3x/T+2hZU1+LLzH+uHTo3Nbz6aqUrqzDJ9IAt8rchvv7CF6XOMJs3V46w6zivVYZ0aVvq8+IkBpq9Bqb3O+NFN3XFzr2Z49crOnrDYQt2LunMHLFjITepVR072MPTIqIfqCXFolZZseJLbSnlaUGqtPfMgI4VPhEIrFvl/ft0S9py/HulX6XPjuvwiLqbU4LOxKmxrJYSMBzAcwEFK6dnyd/UAfA0gA0AOgGsopewSI3qYV67ohIFvOLuD8ILW9R29vhFapNbE8yPOrvRdQlxM2PRgduKtTAkT5F+vo6s79/t/bLNcvhWCt6f7bLk/AO2gY+pvWO5hCOU+MlJK8JwEEL7Om6ZUx/s3nINqCTFoEqTE69iMRx4OXvMeRizyzwAMDfpuLIA5lNLWAObIn6MCp5cj3tm7heaki5soHd1IjsfPF+VYLqdLkzoAgPYNpWBK/wsKoqQ39Fav612wnW/o2GDF4kdFruD0/M+qpwfZLt9q6r5hnRuif7t0tE5PrvR9Sk378Va8QFhFTimdCyDYsTwCwAT57wkALmMrlndxOsJfi9QajDoUZRZG1cwc3GQ5VnXjutZDhNavmYic7GEY1CEd3Q3s4F1nYTu+GULJsDAo5vuoz9ilETzLpQBtQGXrONTj/9d3a0P8Wpm6YdwMPn4Huo5V8zKdUpoHAJTSPEKI7t5mQshoAKMBoGnTphaLix6MvCjevb4b7pu0KuQxf2zONxVAKRRWFlN4ZKGL40xYuMuxa6fVSsI+Rs8wFOpnNefhPjh4ogh7j51R/a7/MH9nGBrab2EojPL93eejeoKzuXYdn+yklI6jlGZSSjNTU1OdLs5x6oTY1qzHFjmYEyv6tg1fjy/N2MS0TLOoFYERzmlaR/P72y+Qlga2NJHijjWh1IvZ8ANmMLNayU5yDQVCpHru1TIl6Np8MKrH2z7lXOyepU+aX1gQCkKkEZ3iLnQKqxb5AUJIQ9kabwjAvxkbdHjjmi4oLKnaSZPiY5FeKxEHThRhYPt0zN4UPpHzEDPhVQ00Zt6Zf3h0ZL25h4s6NURO9jDD13HC9eVlS7EsQHH4VBH6/OdPt0UxBIu2VBQ0V8Ny9JeW7J47yw5WLfKpAEbKf48EMIWNON7hinMa44ae2q4gZaGCkf59xkY8CK9gdqNKYYn/75kXZzeSLDWlhod0rNhJnJkRfn7g6OliPDfVXpTFcE+XpaIMNZr08PvS8xhZfjgJQF8A9QkhuQCeAZAN4BtCyG0AdgO42kkhvYai2IysLDKy0kONkbbMu72b7cevuOzW4UlsDLG1uzNYSb5zfTccPlmMkrIAmtarjhenh67L+yevwoJt4eO7fHdXL1z14aKQx+jGsmE4Jnt+xNm4Nau5posyPsaaXenl6Rhe6Q/DKnJK6fU6P7F1JvkIpd8aGXLHMshS5DaKsmnXILk8eUMo7G668hwhHuHZZ9XCmlzrq2bKR3fy58S4WJwVIh5JMEaUOBB62azii0+K156QY2mRx8fGoE3QEkCFmBiCnOxhuPajRViy0x87sL2CN2K0+gzFAgunyGesyzOcAEPBSJ8xOgQd1qkhpq/LM1W+NsbuV8HKJohzM+qZPscLsAq14rRVGWqyLfvKThjQPs1yzkzWmJ2T2JF/0lZ5vz7Q2/PZnMIhFLkFHhjYGs9N2xhySdFTP63DF4t3V/J5GkE9TF/59CDTccjVVGO85Mlo/5qxbn/4g4IY06+V6XO8gN2gWV4ISJacFI8rztGO9e4GZn3lt02wt3a/bQPtEQILePn9fR1rxSkmjz4v5O+3ZjVHTvYwxMXqV98Xi6Xg82aX4ZWolrPVq5GgmQTXqN/tuxW5psrWQxmWs8g6rkcMo63MLP25RvBKKkAn4X2Lbk96junXktm1GnDa1CUUuQbntUgJf5BDNLcYB9xJLmhVH/93ZSc8NayD26KExajS+fauXvh8lHbi4WBC6RUjcwahiIL3gGl4TRDqMfpCdoo8OMyEUwhF7jBmGuXsh/rgwtbhN/vwtlgIIbi2R9NKrprWOll8rHBtJrvYMkYnyVqm1kTvNqHr+p/9nXf38BxBLH9qoKXzeLt/4txeIGCz+DTVyLU+p1guQpHb4MFBrVErTBo0M0pXL8VZMG5ZceoOzdL//n9XVQ3o7wUeGtzW1GYkI6gz5FzcqQEm3tYTQzqm49bzM5iWowUvpWKXF4KibvqNS7ucxb1MochtkJachHGchk5eQP0C8btLwC2bT72i54N/dEd6rSR8dFNm2IBSbsL7UTepV51ZDPT+7XTDQOnCYsTLKw65gli1YhMvb992krPqJDkeddBJ3HpsPPNyalEtPhYXByUuCUVWqxRsP2gtdKwdpt13AU4WldpO0/jBP84xfQ6LJ/THo3257uoWFrnAMIoV3rhuNSQnORuQ32nMzF2wVPqj5CBgbrHphaF4/Zouho9Pdyn2SHJSPBrWth4KWUFvk5PT1EqKRzrHFI2+V+Tjb8nE5d0auVZ+uOVna23s+tOD9xK74HKjdBDChHoay0m9jlvtDZBWTFnlk5HW3J68g9KxwPeKvH+7dFeX7LnhK04IsX7dSagqNIHffeRuOcld9qwYRpnYJi4/azs6dUB7c5vxysu0XqRr+F6RAwi7csRJ3LBWQm1EchJl9OHHhh6MW0aXX4y9ipe2t4NSCSQiYrLzxvOaISaG4N9TNti+1rd39TJ3QhS1cuVWCSFMXmAzH7gQB08U2b6OFczoU5YbVCgFWqbWwHaLuSetoBeOORTlL21Gt66E6/UDfnnZqokIizwuNgY398pgcq0eJoM3tUp3L3ONXR4b2g6zHuxt+Hhl8uY2RhN27RrUCrspxynM+EGbMVoKp/DTmCwsGNuf6TVDUd/CUrjylzbYuFa+Hm3SQHIRt3eWWiEiFLkC680bRvBrRhEAaJNeE43rGldSNRPjkJM9DDee18z3I5E4E87qpgwVeVJCLJKT4ittDArFa1cbX2HCknLXSgzA4mGHCqMrsE9EKXKBOWIIKR9G+nE4aYd4E/MMt1/QAs9d2pFJuX1NjkCu6m4/KqEVNVyxGsu+Rf7VHT3tXcACcx7uY/lcP/YFocijGVWDNdtZfW6Qm9qYkxAXg5GMttBbWdq25Al7OVysKGLlFBarbM5vaX0JoRWa16/harJuNxCKnAFWdo8F8+DANgwkMceZ4jLL1ocX4mjzZuJt5yK9Fv94Jem1kpCTPQwf3dTd0vlWJqaparLTyfDF4bDy4vOhQW0bocgZYDYLkBb3D2xt+dy2OqmzwlFUWrGF2I/DSd5c2DoVS54YiLv6sAtz6lXUewYmjDoXr7vkq3cDP/YFochVWI5a5vKD79Hc2ouE0ooZ+mhzrfgRnqnYlJj8Q89ugPRaSbiSga/eCm50LbFqxee8c303S+e5/eCtejkC1Lr18cjgttZO9AB2g/27tWXd6EqXYKy0j7YNkpGTPYy7f5sJLuthN+IQRbUir12NTYUnxbtbjVbVCqXUcptvUs/ekrwLW1tTECye2aAO1rZuK1h1ZQnM44abw06ZcTEEd/VtwU4Yg0S1Iv/hnvOR1cp+Wjc3IwFe18N6dh0/zlf+9WhfzH+sn6syuBmkzQqsHvOfj/Q1fc7ix+2tuLGCXd1v5/xRFzRHYhz/iItRrchrV4vHl7eHTrRsFN6B5BWyr+xsw7VCfRfprU71BFObmBSqxcdiZK9mTDaN+a3OWJFhITgdr+TDatx8PjVd2vgU1Yo8luEDd9e4tVZ6QlyM4+5EFiMeFlx+TiM85/MUYlbx48jLDrYtcht64c4+/N0qQJQr8hiPxBS1EtRIjdWOmtmsnuM+yFFZ7iZSUHBDmQ3vbDwTj0Abd1atWKNXixRX3CpAhEQ/tArLtFt2Nsi8fHkn0+e8eW0XLM85KpdtvsxPb+mBpinVQSnFkI7puP5cey8TgcArRKPnK6oVeXys9MQ/vLE7MurbW4XRs3kKZm7Yb/o8M8Gb1FzerTEu7yat7bW0c6882w/BRzf5L4F0XAxBacDbPgOv+NLdWC75wz3n41RRqe3ruFGHlnc7u+hgteVaIYTkEELWEUJWE0KWsxKKF8owaOjZDdCugb14yW9d19XSeTyTN9/cqxm3shT0bs9uB61pMpnI0LMb2CpPj5ap+hOAl3RuiCVPDMA3d/onhCsLYghwTtO6uLC1OyGK7WK1bbo5F8HCR96PUtqVUuoJs+7fwzu4Uq7VJK8s9LjRBqQOJcqr0bnlMwymj0Nxz9s31DYAcrKHYXBHaVfkuc3NxbhnRXnoCAefdT3Vaq3RvaWJvhYMA1bVsbBvwO0Nem4QcZOdl1jdZu8SLCxypZ82CJO124253fNbemPVittMuuM8TLqDzVJXI7x+dRcMtLnxKRztGiTjmsyKfQzK+nqWq8GeG2E+fHC3pnWYlW8Gq8YcC+wqcgrgN0LICkLIaK0DCCGjCSHLCSHL8/PzbRYXHo+4JQ3DQrkq1nU4H53aUuFlkXvFT+w2vVqmoBfHlxrV+ZslMYTgkcEVUTtLy6SS4mLZPfPkpHjDMdl7ZEgjECvK3yy3ZmU4XoYZ7E52ZlFK9xFC0gDMIoRsppTOVR9AKR0HYBwAZGZmOq4+/KY2WFjkZYEAgPCWkFOTMQ1rJyHveKGpc1iFRxBokxQfg6u6N8b0tXm4hVEsdTWdGtXGK1d0qpQIvERuh04lB48hUnwgPb6963xmZQ1sn47Zmw5U+b5h7SQsknerfrogh1l5drFV45TSffL/BwH8COBcFkLZwW8WIAv/aWGJ1IH0/LUKZYGKv1mq9CljsgwdlxgnNbdHh7TFi5fx25wz+yHr2WLC4cX29vhF7XDx2Q1Rv2Yipt13Ac6yGGwrFBNvO7dKNEbFn32OQ64NnnX98UjtKT+eixPMYFmRE0JqEEKSlb8BDAawnpVgVtGr5uoJ3ph0U9OnTSreu8F+UorhXaSNJ8+GSUfmVDKINB3fvGIJXnFO5dgko7Kac7XIW6U5ly3Giwk27uzT0vHNbloTii1Sa2LavRfgiYvbMy5Lwgv790Lp8cu6uTc/Z8ciTwcwnxCyBsBSANMppTPZiGUdrTfmV7f3xLInB1b6rnFd9laKWdo3rIVqDF4wwzufhZzsYWEjElbym3JQQMqL5Y1ruiInexjT+Yv3GbwABTbQeZadGtc2lQ/VCBVp5/hqcq2dufVCxFRS9nW4geUap5TuoJR2kf91pJS+xFIwy2g865gY4slJUN4yNbcQ9MgJWPjqs1rVx6e39mAgjcAKbvQnljuxjfDeDecgJ3sYxt9S4WaxG8veKSJu+aFWA4uNIZ70bQU4D8uvOKeRa1EagYq4K6wstn5t05DsUrS5pU8OwLx/VYTTtZxdyiTLnhyomyG+bvV4dDzL3sY2o7jRm9zqw/3bVSzjTA+zxNctIk+Ra3wX61GL3Or2fKsQEHRraj+/qFX+NbQdcrKHMR16r3tuSPkQeEhHZ9dNq0lLTkKTetXLJ+B4vZRTkxPRTMeFtvLpQZh27wVc5HBjktcLPnKvEnmKXKOBxWlY5F2b1OEkUWU+vLHCtzumXyuuZaurwHtTdPZxw2Lz0mQnIYRbRM/gUhLinFclevfWOq0mZj5woePle5mIC5ql9agb1alWpZO/5lJW8KFnV0ygVE/gW/0E/tswZQQtVVqvRgKOnCrmLgsPvLbk8feH+6AWh1VIevsksq/sbDtWkt+JPEWu8axTaiYioNpJ0LRedUe20/Zvl4ayAMVfW7V3sDq1vtYoagXgIUOSGepnX6d6PFdFzrM6vaDG1YYRy9gqodB6ga15ZjCXpaz39W+F4tKA7u9ur6KKPEWu08x5GDHjb+mBb5fv0VXkSkP84B/nWM6IbgcCoH2DZMzaeABptRK5l+806mc/8baeePqn9bjjQk4ZWzhqci8Y5DEcnbKK0RE8tTK4Qzq3/QgPD24b8vdhLicRiTxF7lDYVKMY6c8Xd3LnoRMC3D+wDfq0TcM5Lk56OoV6WWOjOtUw/hZ+yxN5xqL2gmuFZWAsL5fpF6JGkXMjRH92WzRCCGIJ0L0ZGyU+slcz3V2dbpCc6F78lkh0VYWC95puwDupGb1I5K1aCaEu7+7bkqMkVXH9JcOY50aczX3ljSayEs1qXd89EaJMkfspc080EHmKPMTDvkdW5Nf2aKJ/kE3cTPekx03n8c8M5AbCYItsgleeeUWxu7UpTU3kKfIQvyUnxWPbSxeVK/Ro4fkRHbHtpYvcFsMxvPDy5L1LN5Kfpx7BPnKvZAJa/cxgt0WIQEUe5jUdFxvj6LDQi0NsQohjMaIVvr+bXSxoq7jRsd163E4/Tz1+e7A3/u/KTq6UHewj94pF7sZ8QTDujwkYE1ylvHd8eVCPc4HVBKoVvPjy5MH8x/qBUuDCV//gVmab9GS0SU/mVh5QMeKqYpG7rz89Q+QpctXD7dqkDtpybnSh8MpQUMAQWuk/rjSuGzpscaRRxSIX/amciHat/DQmyxNrbsvhKIrbO80EAtZ4wIPhWSJOkbtNqGH+JRx3f7m908wN3Hhne2GiNVrwkk3mNSJSkXdtUgdvX9fVbTEq8dmtPXBjhC8D/NullRRu+siVsvu0SXUl7EJUINdxleiWLiv20b1b4MbzmrorhEzE+cgByaXiFnoWWkKcs6tlvADrFF9mcbN269VIwIKx/ZExdrqLUkQmpXLAu+D25XZvYp2b1A4RaZELogs33RvRumKGJ2VyJQcv84t0w8gMEWmRexExwx7ZKE93eOeGnlopFQmUlUmKPEG2yJMT41BQVIrqDoSi9itCkQt8jxJq3g0LLXg08J5Lq4WqJ0SuUlNcK3Gx0vMdenYDNKydhNt4hSj2AUKRMyZ4qN2uQTI27y/gNuO+YGx/nCku41OYR6A6Q28+ZUv/uznK/+X+C5FS072k2k4zuGM6Zm86gLYNkvHnlnzEEIKHwsQHjzaEj9xheFuJjepUQ6s0PhlbtBjZi//KnED5qgbuRatwr/D2DWshLdk74YRZc01mE2x+YSiap9QAIJZ8aiEUOWP0mli0eMifuaQj9zKVgFVuxKsWKoUPSfGx5csPxQRzVYQidxgvZVmPVMpkk7zKOmOOiAUUHJDrOCC6VBWEIneYgsJSAHAk2bMXcWV3pYuuFeW5xon9445TbpGLcVAVxGSnQ1zYuj6yWtXH18v2AACSk6Kjqt1YOVLuWnGh7Ocv7YiMlOro2zaNe9nRhvJ0xSC3KsIiZ43cyprWq467+rREaSAAAIjjmXY8yhjSsQEAIKN+De5l162RgIcHt/VETOpIR+lCwl1ZlegwE11AMQ6VzQyxsaKjO8XNvZrhqu6NUcMDKbcEznFh61TUrR6P28X68SrYMhMJIUMJIVsIIdsIIWNZCeVngm2FEmUzg7DYHIMQIpR4FFC/ZiJW/Xswzm5U221RPIfl1k8IiQXwPoBBAHIBLCOETKWUbmQlnJ9RtuRf3q0Rxs3dgVpJ8S5LFB3Mfqi368G7BALe2DFjzgWwjVK6AwAIIZMBjAAQ1Ypc8YUrymTs0Ha4f0BrVIvgLdTBtEqridEuDX9bpYk4J4Low44ibwRgj+pzLoCewQcRQkYDGA0ATZt6I3avk1zVvTF2HT6Fe/u3AiBtUnFr2P/FbT1x+FQR93JnP9SHe5kCQTRjR8NoOX2rTCdTSscBGAcAmZmZET/dnBAXg8c9Eqf4gtb13RZBIBBwwI4zMRdAE9XnxgD22RNHIBAIBGaxo8iXAWhNCGlOCEkAcB2AqWzEEggEAoFRLLtWKKWlhJB7AfwKIBbAeErpBmaSCQQCgcAQtmbhKKUzAMxgJItAIBAILCAW3AoEAoHPEYpcIBAIfI5Q5AKBQOBzhCIXCAQCn0N4hoQkhOQD2GXx9PoADjEUxymEnOzwg4yAkJMlfpAR4C9nM0ppqt6PXBW5HQghyymlmW7LEQ4hJzv8ICMg5GSJH2QEvCencK0IBAKBzxGKXCAQCHyOnxT5OLcFMIiQkx1+kBEQcrLEDzICHpPTNz5ygUAgEGjjJ4tcIBAIBBoIRS4QCAR+h1Jq6R+A8QAOAliv+q4LgEUA1gGYBqCW/H08gAny95sAPK465yVImYZOhimvu3z+NgDvoMIt1BvASgClAK4KIecGAF/L56+Tz1HknAXgGIDpWnICqC7/tlm+TrYFOW8BkA9gtfzvdh05d6ju5+Gg+uwA4DdZtmOyPMH1ORPAGlnODwHEmpSzGYA5ANYC+BNAY61nDuAhSGn9tgI4LssyDUAtAK/K5R+DtNY2WMY/AWxR1UWaSRmVstfKsjazUJd3Avhb/jc/+JnL10mA5AvdKt/flWbklH+7RpZ1A4CvdOTMU93PEgArVHKWqeppT7CcAJJVv6+W6/stHTk1+xpC9KGgZ54IqQ/tBlCgeubDVOUfARCQy1HX5bXy/W0A8KqF/nOX/P1q+Xl1MFmXfwFYKpe/DsAf8v9rAPQ18iwNytlUvvYqWYaLdc5X6nKbLGdG0O+1AOwF8J4hfWxDkfcGcA4qK/JlAPrIf48C8IL89w0AJquUYo4iOIDzADQMblwa5S0F0AtSZqJfAFwkf58BoDOAz4MbYZCc+wB8KH+3HcDvKjknArgEUmOuIqf8dz9V556nlG9CzltCPRSVnFtU97MtqD5zICW7vgHAd7JcwfWpvDwJgO8BXGdSzm8BjJT/7g9gotYzB9BPLnsZgDfkRjkKwKcAFgD4h/zdIgBDgmT8E0CmgTamJ2M/ANXlv+8G8LXJurwPwFEA9QDcAeAkgLoadfkcgBflv2MA1DcpZ2tIHbqu/DlNR86dqvvJQeW2WRyuDwVdcwWA3jpyavY1hOhDQc/8HkjGwTK5bpRnru7nP0BS5imo6D8pkJR/qnzcBAADTNZlLdUxlwKYabIuHwfwvvz3EwBOA6gDIE2us5hQ5ZuQcxyAu+W/OwDI0Tn/HlToo+tQtQ2/DeArGFTkll0rlNK58gNT0xbAXPnvWQCuVA4HUIMQEgegGoBiACfk6yymlOaFKosQ0hDSg1xEpbv8HMBl8vk5lNK1kKyAUHImQ2pAAJAKoDMhhMhydodkYUBLTkrpaUrpH/L1iiEp/MZm5AyHSs4S1f2chYr6zIGkCGZBqs9EWb7g+jwhHx8H6aVTZTY7jJwdIFm5gGRZjNCQEZTSPyilpyE984lyfcwC0BdAEqQY9cmQRmPH1TIaIcwzV8oGgMUIehYG6jIgH3cEkhI/DOBiBNUlJCX1inxsgFJaZSdfmLq8A5LyOCpf46COnKdU91Mf0rMFpPpUQk3r9iGVLK0hKaZ5wXLK5Wn2tVB9KKifj4DUh9oCeAHAAFTt5y0hjQqhkrEFgK2U0nz5+9mqc9Tyh3rm6nutgaB2baAuv4BkAABSvuF8SC+Wg5BGjplG+2+Y4ygkaxoAakM/a5pSl4BklA2Q9REIId0BpEMafRuCtY98PaS3JQBcjYpUcN8BOAVp2LMbwGtyJzJKI0ip5RRy5e/MEI+KZNHrAZRAshTUcuaFk5MQUgeS9T4HVQkn55WEkLWEkO8IIU0Qnj2oqM8bASQQQn4A8C8ArfTkJIT8CmmYWQCp7s3IuQYVnexyAMmEkJQQMq4H8CIkq+RqSJ3nD0jDzYEA2kOqq+C6/JQQspoQ8rTSgE3IqOY2uexwqOtyCCSrFpDq5ziAj6CqS/k5A8ALhJCVhJBvCSHpJuVsA6ANIWQBIWQxIWSoATkLIFmVgFSfhBCyHMADkCzIUH3oekiWXZWXNyOUhOvrIblTjkMaaar7eQP5N7WM2wC0I4RkyC+iy1A5TaT6+rrPnBAyhhCyHZLr7p8G5A2uS6XM45BGYDmEkOaQDLkm4co3KOezAG4khORCytVwn45s5cnrKaWlskwphJAYAK8DeNTA/ZXDWpGPAjCGELICkjVWLH9/LiRf31kAmgN4mBDSwsR1DSV6NilnbUiWgVrOOgghp9wIJwF4h1K6w6Sc0yANhTvL5U7QODaY91FRnzUgPa9HANwvf35SS05K6RBIQ+hESO4RM3I+AqAPIWQVgD6Q/HSlIWT8EUAWgCsg1WUpJOV9lfzbOkgKRi3jPyilnQBcKP+7yaSM0gGE3AggE8B/QsinoK7LREjPGZDaJoXkKlDXZRwkS38BpfQcSC6i10zKGQfJvdIXUh18rHpBVL2QdD8HAKSr+tBRKm0Ffw1ANwAXQL8PXQepfTqFcq+jAIyBVD81UNF/LoLUrxqoZZRHJHdDcsXMgzS61GpTIZ85pfR9SmlLAI8BeCqkoNp1WSxb01dCmvNaBuAtAAtleYzqmVDHXQ/gM0ppY0ijvImycjZ6jXsAzKCU7tH4XRemipxSuplSOphS2h1Sg9ou/3QDJJ9WiTyUWQCpA2pCCImVrbXVhJDnIb3x1MPnsImeCSEvKdeQvypBxRt5GyQfWbcgORuFkXMcgL8ppW+ZlZNSephSWiR//z9IVoCWnGr2qerzO0i+zR2QJo5mAOiiV5+U0kJIOVRHmJRzH6X0CkppN0gvClBKjytyQpURihAyEFKnbiMru0mQrKDFkKz5n+Xj26llpJTulf8vgOQHPNfsM5fLfhLApUq9mqjLmZBcKoDUNg8DyA2qy8OQ2siP8nHfAjjHpJy5AKbI7WknJJ99ay05VfczmFI6SNWHtsmH9IXk0uuk9cwJIV0AxFFKV8ifg+U0jcYzzwXQhFK6GZKSKoA0yaj0n0cBLKKUngmWkVI6jVLak1LaS66Hv23088mQXRkm63InJAX+FKX0ekppV0rpCEgG3N965ZuU8zYA38j3vAiSm7G+hpzlyetlA7E2JNdQLwD3EkJyIL28byaEZGvUQWWoAUe63j9IExnqyc40WjEx9DmAUfLnxyBNghFIb/CNADoHXSvcZOcySJM1yuTCxUG/fwaNyU6VnOrJztFyZZfLCamjbNKTE5L74HvIkyJm5QTQUHXM5QAWh6pP+X6U+ouB5IfeDcm//xikhjdGLSeAmko5kKzBrwHca1LO+qiY+HkJwPNaMkJ6CW4H0DPomf8X0ojjcfke5kCyzhUZ4yBPGkJyd30H4C6TMipltzbSNjXqcjIkH2ldSEPhAkgTn8HPfDKA/vLftwD41qScQwFMUNXrHgApGnJuU+4HlfvQZACj5c/PQRp+dwiWU/49G8BzBvutZl+DTh9SPfMxkCY70yBZ/9+gcj/fLd+/Vv9R7qsupJUnbUzWZWvVMZcAWK4jp15dfiHL8wAkt1oN+bdBAOYa1TMG5PwFwC3y3+0h6Z0qK1+UupT/vg7ANxrH3AIOq1YmQfLXlUB6u9wGaci/Vf6XrdwAJAXzLaSlPxsBPKq6zqvy+QH5/2d1ysuUG9N2AO+prt1DPu8UJCtqQwg5T0Mabu2C9HZW5JwHqWOfkY/JUcsJ6Y1LISn61dBYPmhAzlfk+18DyYfcTkfOUvlfkXxPRSo5B6FiCZcio1rOdLmBKce8C8lKMyPnVZBeElsBfAwgUacuCyEpllz575OyjLGQ/M2bIU10HQqSsQakVQKKjG9Df4mknoyz5eeoPIupFupyFCo6/TJot81mkCZIlWWOTU3KSSCt6NkIycV0nY6cAUiunt1yfZ6U5ZyIiiVyG/TklK+1A0FtSkNOzb6GEH0IVfv5MlT0lZ1yXRJUGEt6/XwSKtqr5kqqMHX5tnzd1ZD6T0eTdTlNvofVsgyFcp3Nhmr5ql75JuTsAGkkskYua7DO+UlyXW2DtAKmhR1FLrboCwQCgc9hPdkpEAgEAs4IRS4QCAQ+RyhygUAg8DlCkQsEAoHPEYpcIBAIfI5Q5IKIhRBSJm/C2EAIWUMIeUhnl536nAxCyA28ZBQIWCAUuSCSOUOl3XsdIa3BvxjAM2HOyYC021Mg8A1iHbkgYiGEnKSU1lR9bgFpQ0t9SJt9JkLaoARIO2AXEkIWQ9qRtxNSPJx3IG166QspRsv7lNKPuN2EQGAAocgFEUuwIpe/Owop9ksBgACltJBI4V8nUUozCSF9ATxCKR0uHz8a0lbvFwkhiZB27V1NpdgpAoEniAt/iEAQUShR5+IBvEcI6QppS3cbneMHQ4pdf5X8uTakOB5CkQs8g1DkgqhBdq2UQYrV/gykeC1dIM0VFeqdBuA+SumvXIQUCCwgJjsFUQEhJBVS5L73qORPrA0gj1IagBQPPVY+tABS7GqFXwHcTQiJl6/ThhBSAwKBhxAWuSCSqSbHf46HFAVxIqRohADwAYDvCSFXQ4qmd0r+fi2AUkLIGkhhXd+GtJJlJSGEQIr8dxkf8QUCY4jJToFAIPA5wrUiEAgEPkcocoFAIPA5QpELBAKBzxGKXCAQCHyOUOQCgUDgc4QiFwgEAp8jFLlAIBD4nP8HkkPu4sfPvqwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pandas import read_csv\n",
    "from matplotlib import pyplot\n",
    "series = read_csv('daily-min-temperatures.csv', header=0, index_col=0)\n",
    "series.plot()\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0f6dc2e",
   "metadata": {},
   "source": [
    " # Correlation and Autocorrelation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5269ea89",
   "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": [
    "from pandas import read_csv\n",
    "from matplotlib import pyplot\n",
    "from statsmodels.graphics.tsaplots import plot_acf\n",
    "series = read_csv('daily-min-temperatures.csv', header=0, index_col=0)\n",
    "plot_acf(series)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4c69b1dd",
   "metadata": {},
   "source": [
    "# Partial Autocorrelation Function\n",
    "\n",
    "_A partial autocorrelation is a summary of the relationship between an observation in a time series with observations at prior time steps with the relationships of intervening\n",
    "observations removed_. \n",
    "\n",
    "The partial autocorrelation at lag k is the correlation that results\n",
    "after removing the effect of any correlations due to the terms at shorter lags.\n",
    "\n",
    "The autocorrelation for an observation and an observation at a prior time step is comprised of both the **direct correlation and indirect correlations**. _These indirect correlations are a linear function of the correlation of the observation, with observations\n",
    "at intervening time steps_. It is these indirect correlations that the partial autocorrelation\n",
    "function seeks to remove. This is the intuition for the **partial autocorrelation**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "93002c5b",
   "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": [
    "from pandas import read_csv\n",
    "from matplotlib import pyplot\n",
    "from statsmodels.graphics.tsaplots import plot_pacf\n",
    "series = read_csv('daily-min-temperatures.csv', header=0, index_col=0)\n",
    "plot_pacf(series, lags=50)\n",
    "pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04a77df3",
   "metadata": {},
   "source": [
    "# Calculating Autocorrelation and Partial Autocorrelation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b115e4e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from statsmodels.graphics.tsaplots import plot_acf, plot_pacf\n",
    "from statsmodels.tsa.stattools import acf, pacf\n",
    "from statsmodels.tsa.tsatools import lagmat\n",
    "import matplotlib.pyplot as plt\n",
    "# settings\n",
    "plt.style.use(\"seaborn\")\n",
    "plt.rcParams[\"figure.figsize\"] = (16, 8)\n",
    "%config InlineBackend.figure_format = \"retina\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ec40bb7",
   "metadata": {},
   "source": [
    "# Importing dataset and plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "024d3a08",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1152x576 with 2 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 939
      }
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1152x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 480,
       "width": 939
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = pd.read_csv(\"airline-passengers.csv\", index_col=0)\n",
    "df.index = pd.to_datetime(df.index)\n",
    "y = df[\"Passengers\"]\n",
    "y\n",
    "\n",
    "fig, ax = plt.subplots(2, 1)\n",
    "plot_acf(df, ax=ax[0])\n",
    "plot_pacf(df, ax=ax[1], method=\"ols\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e716366",
   "metadata": {},
   "source": [
    "**Autocorrelation Function (ACF)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "58796e8a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.        , 0.94804734, 0.87557484, 0.80668116, 0.75262542,\n",
       "       0.71376997, 0.6817336 , 0.66290439, 0.65561048, 0.67094833,\n",
       "       0.70271992])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "acf(y, nlags=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b191d31",
   "metadata": {},
   "source": [
    "# Replicating it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "72c8f46d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.        , 0.94804734, 0.87557484, 0.80668116, 0.75262542,\n",
       "       0.71376997, 0.6817336 , 0.66290439, 0.65561048, 0.67094833,\n",
       "       0.70271992])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# benchmark\n",
    "acf(y, nlags=10)\n",
    "# replicating the acf function\n",
    "acf_list = []\n",
    "mu = y.mean()\n",
    "for lag in range(0, 11):\n",
    "    acf_list.append(np.dot((y - mu).iloc[lag:], (y.shift(lag) - mu).iloc[lag:]) / sum((y - mu)** 2))\n",
    "np.array(acf_list)\n",
    "# alternative way to write the same using sum instead of the dot product\n",
    "acf_list = []\n",
    "mu = y.mean()\n",
    "for lag in range(0, 11):\n",
    "    acf_list.append(sum((y - mu).iloc[lag:] * (y.shift(lag) - mu).iloc[lag:]) / sum((y - mu)** 2))\n",
    "np.array(acf_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d40324b4",
   "metadata": {},
   "source": [
    "# Partial Autocorrelation Function (PACF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a72c59a8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  0.95893198, -0.32983096,  0.2018249 ,  0.14500798,\n",
       "        0.25848232, -0.02690283,  0.20433019,  0.15607896,  0.56860841,\n",
       "        0.29256358])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pacf(df, nlags=10, method=\"ols\")\n",
    "N_LAGS = 10\n",
    "# the first partial autocorrelation is always equal to 1\n",
    "pacf_list = [1]\n",
    "X = pd.DataFrame(lagmat(y, N_LAGS))\n",
    "X.columns = [f\"lag_{lag+1}\" for lag in range(10)]\n",
    "for k in range(1, N_LAGS + 1):\n",
    "    fitted_model = LinearRegression().fit(X.iloc[k:, :k],y.iloc[k:])\n",
    "    pacf_list.append(fitted_model.coef_[-1])\n",
    "np.array(pacf_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db913110",
   "metadata": {},
   "source": [
    "Below you can see how the PACF values change when including more lags using the inefficient method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c9b521aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  0.95868964, -0.33258806])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pacf(y, 2, method=\"ols-inefficient\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "5f557a16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  0.95860315, -0.33427195,  0.1970437 ,  0.13909745])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pacf(y, 4, method=\"ols-inefficient\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59f49175",
   "metadata": {},
   "source": [
    "For comparison's sake, we run the same two calls to the pacf function using the efficient method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8a611d30",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  0.95893198, -0.32983096])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pacf(y, 2, method=\"ols\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4bd388df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        ,  0.95893198, -0.32983096,  0.2018249 ,  0.14500798])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pacf(y, 4, method=\"ols\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a6783d9",
   "metadata": {},
   "source": [
    "# Autocorrelation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "fbe33163",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[100.33255144]\n"
     ]
    }
   ],
   "source": [
    "# AR example\n",
    "from statsmodels.tsa.ar_model import AutoReg\n",
    "from random import random\n",
    "# contrived dataset\n",
    "data = [x + random() for x in range(1, 100)]\n",
    "# fit model\n",
    "model = AutoReg(data, lags=1)\n",
    "model_fit = model.fit()\n",
    "# make prediction\n",
    "yhat = model_fit.predict(len(data), len(data))\n",
    "print(yhat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64b862c5",
   "metadata": {},
   "source": [
    "# Moving Average"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9112755c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[70.90071956]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Admin\\AppData\\Roaming\\Python\\Python38\\site-packages\\statsmodels\\tsa\\statespace\\sarimax.py:978: UserWarning: Non-invertible starting MA parameters found. Using zeros as starting parameters.\n",
      "  warn('Non-invertible starting MA parameters found.'\n"
     ]
    }
   ],
   "source": [
    "# MA example\n",
    "from statsmodels.tsa.arima.model import ARIMA\n",
    "from random import random\n",
    "# contrived dataset\n",
    "data = [x + random() for x in range(1, 100)]\n",
    "# fit model\n",
    "model = ARIMA(data, order=(0, 0, 1))\n",
    "model_fit = model.fit()\n",
    "# make prediction\n",
    "yhat = model_fit.predict(len(data), len(data))\n",
    "print(yhat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91d1c514",
   "metadata": {},
   "source": [
    "# Autoregressive Moving Average (ARMA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5052715b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.50984503]\n"
     ]
    }
   ],
   "source": [
    "# ARMA example\n",
    "from statsmodels.tsa.arima.model import ARIMA\n",
    "from random import random\n",
    "# contrived dataset\n",
    "data = [random() for x in range(1, 100)]\n",
    "# fit model\n",
    "model = ARIMA(data, order=(2, 0, 1))\n",
    "model_fit = model.fit()\n",
    "# make prediction\n",
    "yhat = model_fit.predict(len(data), len(data))\n",
    "print(yhat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "597f5ea2",
   "metadata": {},
   "source": [
    "# Autoregressive Integrated Moving Average (ARIMA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "63c0c590",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[100.85733426]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Admin\\AppData\\Roaming\\Python\\Python38\\site-packages\\statsmodels\\tsa\\statespace\\sarimax.py:966: UserWarning: Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.\n",
      "  warn('Non-stationary starting autoregressive parameters'\n",
      "C:\\Users\\Admin\\AppData\\Roaming\\Python\\Python38\\site-packages\\statsmodels\\tsa\\statespace\\representation.py:374: FutureWarning: Unknown keyword arguments: dict_keys(['typ']).Passing unknown keyword arguments will raise a TypeError beginning in version 0.15.\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "# ARIMA example\n",
    "from statsmodels.tsa.arima.model import ARIMA\n",
    "from random import random\n",
    "# contrived dataset\n",
    "data = [x + random() for x in range(1, 100)]\n",
    "# fit model\n",
    "model = ARIMA(data, order=(1, 1, 1))\n",
    "model_fit = model.fit()\n",
    "# make prediction\n",
    "yhat = model_fit.predict(len(data), len(data), typ='levels')\n",
    "print(yhat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "afeafc33",
   "metadata": {},
   "source": [
    "# Seasonal Autoregressive Integrated Moving-Average (SARIMA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "368bacf7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[100.75505008]\n"
     ]
    }
   ],
   "source": [
    "# SARIMA example\n",
    "from statsmodels.tsa.statespace.sarimax import SARIMAX\n",
    "from random import random\n",
    "# contrived dataset\n",
    "data = [x + random() for x in range(1, 100)]\n",
    "# fit model\n",
    "model = SARIMAX(data, order=(1, 1, 1), seasonal_order=(0, 0, 0, 0))\n",
    "model_fit = model.fit(disp=False)\n",
    "# make prediction\n",
    "yhat = model_fit.predict(len(data), len(data))\n",
    "print(yhat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db36129c",
   "metadata": {},
   "source": [
    "# Seasonal Autoregressive Integrated Moving-Average with Exogenous Regressors (SARIMAX)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "c67d038f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[100.94702892]\n"
     ]
    }
   ],
   "source": [
    "# SARIMAX example\n",
    "from statsmodels.tsa.statespace.sarimax import SARIMAX\n",
    "from random import random\n",
    "\n",
    "# contrived dataset\n",
    "data1 = [x + random() for x in range(1, 100)]\n",
    "data2 = [x + random() for x in range(101, 200)]\n",
    "\n",
    "# fit model\n",
    "model = SARIMAX(data1, exog=data2, order=(1, 1, 1), seasonal_order=(0, 0, 0, 0))\n",
    "model_fit = model.fit(disp=False)\n",
    "\n",
    "# make prediction\n",
    "exog2 = [200 + random()]\n",
    "yhat = model_fit.forecast(steps=1, exog=[exog2])\n",
    "print(yhat)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0dfbafa",
   "metadata": {},
   "source": [
    "# Simple Exponential Smoothing (SES)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "27477f24",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[99.5137712]\n"
     ]
    }
   ],
   "source": [
    "# SES example\n",
    "from statsmodels.tsa.holtwinters import SimpleExpSmoothing\n",
    "from random import random\n",
    "# contrived dataset\n",
    "data = [x + random() for x in range(1, 100)]\n",
    "# fit model\n",
    "model = SimpleExpSmoothing(data)\n",
    "model_fit = model.fit()\n",
    "# make prediction\n",
    "yhat = model_fit.predict(len(data), len(data))\n",
    "print(yhat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5857912",
   "metadata": {},
   "source": [
    "# Holt Winter’s Exponential Smoothing (HWES)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "d79c3b8e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[99.56846059]\n"
     ]
    }
   ],
   "source": [
    "# HWES example\n",
    "from statsmodels.tsa.holtwinters import ExponentialSmoothing\n",
    "from random import random\n",
    "# contrived dataset\n",
    "data = [x + random() for x in range(1, 100)]\n",
    "# fit model\n",
    "model = ExponentialSmoothing(data)\n",
    "model_fit = model.fit()\n",
    "# make prediction\n",
    "yhat = model_fit.predict(len(data), len(data))\n",
    "print(yhat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e865b3a0",
   "metadata": {},
   "source": [
    "# Vector Autoregression (VAR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "c0d9b041",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[100.00328175 100.40508675]]\n"
     ]
    }
   ],
   "source": [
    "# VAR example\n",
    "from statsmodels.tsa.vector_ar.var_model import VAR\n",
    "from random import random\n",
    "\n",
    "# contrived dataset with dependency\n",
    "data = []\n",
    "for i in range(100):\n",
    "    v1 = i + random()\n",
    "    v2 = v1 + random()\n",
    "    row = [v1, v2]\n",
    "    data.append(row)\n",
    "\n",
    "# fit model\n",
    "model = VAR(data)\n",
    "model_fit = model.fit()\n",
    "\n",
    "# make prediction\n",
    "yhat = model_fit.forecast(model_fit.endog, steps=1)\n",
    "print(yhat)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "801c6e0f",
   "metadata": {},
   "source": [
    "# Vector Autoregression Moving-Average (VARMA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "0ea951ed",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Admin\\AppData\\Roaming\\Python\\Python38\\site-packages\\statsmodels\\tsa\\statespace\\varmax.py:161: EstimationWarning: Estimation of VARMA(p,q) models is not generically robust, due especially to identification issues.\n",
      "  warn('Estimation of VARMA(p,q) models is not generically robust,'\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.45964459 1.04999937]]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Admin\\AppData\\Roaming\\Python\\Python38\\site-packages\\statsmodels\\base\\model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n"
     ]
    }
   ],
   "source": [
    "# VARMA example\n",
    "from statsmodels.tsa.statespace.varmax import VARMAX\n",
    "from random import random\n",
    "# contrived dataset with dependency\n",
    "data = list()\n",
    "for i in range(100):\n",
    "    v1 = random()\n",
    "    v2 = v1 + random()\n",
    "    row = [v1, v2]\n",
    "    data.append(row)\n",
    "# fit model\n",
    "model = VARMAX(data, order=(1, 1))\n",
    "model_fit = model.fit(disp=False)\n",
    "# make prediction\n",
    "yhat = model_fit.forecast()\n",
    "print(yhat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fea69383",
   "metadata": {},
   "source": [
    "# Vector Autoregression Moving-Average with Exogenous Regressors (VARMAX)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "5ce31ea2",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Admin\\AppData\\Roaming\\Python\\Python38\\site-packages\\statsmodels\\tsa\\statespace\\varmax.py:161: EstimationWarning: Estimation of VARMA(p,q) models is not generically robust, due especially to identification issues.\n",
      "  warn('Estimation of VARMA(p,q) models is not generically robust,'\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.45416053 1.22619293]]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Admin\\AppData\\Roaming\\Python\\Python38\\site-packages\\statsmodels\\base\\model.py:607: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  warnings.warn(\"Maximum Likelihood optimization failed to \"\n",
      "C:\\Users\\Admin\\AppData\\Roaming\\Python\\Python38\\site-packages\\statsmodels\\tsa\\statespace\\varmax.py:161: EstimationWarning: Estimation of VARMA(p,q) models is not generically robust, due especially to identification issues.\n",
      "  warn('Estimation of VARMA(p,q) models is not generically robust,'\n",
      "C:\\Users\\Admin\\AppData\\Roaming\\Python\\Python38\\site-packages\\statsmodels\\tsa\\statespace\\varmax.py:161: EstimationWarning: Estimation of VARMA(p,q) models is not generically robust, due especially to identification issues.\n",
      "  warn('Estimation of VARMA(p,q) models is not generically robust,'\n"
     ]
    }
   ],
   "source": [
    "# VARMAX example\n",
    "from statsmodels.tsa.statespace.varmax import VARMAX\n",
    "from random import random\n",
    "# contrived dataset with dependency\n",
    "data = list()\n",
    "for i in range(100):\n",
    "    v1 = random()\n",
    "    v2 = v1 + random()\n",
    "    row = [v1, v2]\n",
    "    data.append(row)\n",
    "    data_exog = [x + random() for x in range(100)]\n",
    "# fit model\n",
    "model = VARMAX(data, exog=data_exog, order=(1, 1))\n",
    "model_fit = model.fit(disp=False)\n",
    "# make prediction\n",
    "data_exog2 = [[100]]\n",
    "yhat = model_fit.forecast(exog=data_exog2)\n",
    "print(yhat)"
   ]
  }
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