{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "block_hidden": true
   },
   "outputs": [],
   "source": [
    "%load_ext rpy2.ipython\n",
    "%matplotlib inline\n",
    "from fbprophet import Prophet\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import logging\n",
    "logging.getLogger('fbprophet').setLevel(logging.ERROR)\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "df = pd.read_csv('../examples/example_wp_peyton_manning.csv')\n",
    "df['y'] = np.log(df['y'])\n",
    "m = Prophet()\n",
    "m.fit(df)\n",
    "future = m.make_future_dataframe(periods=366)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "block_hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Initial log joint probability = -19.4685\n",
       "Optimization terminated normally: \n",
       "  Convergence detected: relative gradient magnitude is below tolerance\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%R\n",
    "library(prophet)\n",
    "df <- read.csv('../examples/example_wp_peyton_manning.csv')\n",
    "df$y <- log(df$y)\n",
    "m <- prophet(df)\n",
    "future <- make_future_dataframe(m, periods=366)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prophet includes functionality for time series cross validation to measure forecast error using historical data. This is done by selecting cutoff points in the history, and for each of them fitting the model using data only up to that cutoff point. We can then compare the forecasted values to the actual values. This figure illustrates a simulated historical forecast on the Peyton Manning dataset, where the model was fit to a initial history of 5 years, and a forecast was made on a one year horizon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "input_hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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S1WVPIowgdKTrioroGKl0N6YCl8sFSZLAGIMkSWhoaEj1JXUa2dz2TMXs1uxwUIkKgtBh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\n1gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9d27e0d10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from fbprophet.diagnostics import cross_validation\n",
    "df_cv = cross_validation(\n",
    "    m, '365 days', initial='1825 days', period='365 days')\n",
    "cutoff = df_cv['cutoff'].unique()[0]\n",
    "df_cv = df_cv[df_cv['cutoff'] == cutoff]\n",
    "\n",
    "fig = plt.figure(facecolor='w', figsize=(10, 6))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(m.history['ds'].values, m.history['y'], 'k.')\n",
    "ax.plot(df_cv['ds'].values, df_cv['yhat'], ls='-', c='#0072B2')\n",
    "ax.fill_between(df_cv['ds'].values, df_cv['yhat_lower'],\n",
    "                df_cv['yhat_upper'], color='#0072B2',\n",
    "                alpha=0.2)\n",
    "ax.axvline(x=cutoff, c='gray', lw=4, alpha=0.5)\n",
    "ax.set_ylabel('y')\n",
    "ax.set_xlabel('ds')\n",
    "ax.text(x=pd.to_datetime('2010-01-01'),y=12, s='Initial', color='black',\n",
    "       fontsize=16, fontweight='bold', alpha=0.8)\n",
    "ax.text(x=pd.to_datetime('2012-08-01'),y=12, s='Cutoff', color='black',\n",
    "       fontsize=16, fontweight='bold', alpha=0.8)\n",
    "ax.axvline(x=cutoff + pd.Timedelta('365 days'), c='gray', lw=4,\n",
    "           alpha=0.5, ls='--')\n",
    "ax.text(x=pd.to_datetime('2013-01-01'),y=6, s='Horizon', color='black',\n",
    "       fontsize=16, fontweight='bold', alpha=0.8);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[The Prophet paper](https://peerj.com/preprints/3190.pdf) gives further description of simulated historical forecasts.\n",
    "\n",
    "This cross validation procedure can be done automatically for a range of historical cutoffs using the `cross_validation` function. We specify the forecast horizon (`horizon`), and then optionally the size of the initial training period (`initial`) and the spacing between cutoff dates (`period`). By default, the initial training period is set to three times the horizon, and cutoffs are made every half a horizon.\n",
    "\n",
    "The output of `cross_validation` is a dataframe with the true values `y` and the out-of-sample forecast values `yhat`, at each simulated forecast date and for each cutoff date. This dataframe can then be used to compute error measures of `yhat` vs. `y`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "output_hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Initial log joint probability = -53.0208\n",
       "Optimization terminated normally: \n",
       "  Convergence detected: relative gradient magnitude is below tolerance\n",
       "          ds         y     yhat yhat_lower yhat_upper     cutoff\n",
       "1 2014-01-21 10.542574 9.439116   8.827709  10.077209 2014-01-20\n",
       "2 2014-01-22 10.004283 9.266698   8.635896   9.888154 2014-01-20\n",
       "3 2014-01-23  9.732818 9.263058   8.645846   9.861981 2014-01-20\n",
       "4 2014-01-24  9.866460 9.277099   8.666444   9.847888 2014-01-20\n",
       "5 2014-01-25  9.370927 9.087197   8.440665   9.734763 2014-01-20\n",
       "6 2014-01-26  9.490545 9.460199   8.826654  10.070429 2014-01-20\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%R\n",
    "df.cv <- cross_validation(m, horizon = 730, units = 'days')\n",
    "head(df.cv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ds</th>\n",
       "      <th>yhat</th>\n",
       "      <th>yhat_lower</th>\n",
       "      <th>yhat_upper</th>\n",
       "      <th>y</th>\n",
       "      <th>cutoff</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2014-01-21</td>\n",
       "      <td>9.439510</td>\n",
       "      <td>8.799215</td>\n",
       "      <td>10.080240</td>\n",
       "      <td>10.542574</td>\n",
       "      <td>2014-01-20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2014-01-22</td>\n",
       "      <td>9.267086</td>\n",
       "      <td>8.645900</td>\n",
       "      <td>9.882225</td>\n",
       "      <td>10.004283</td>\n",
       "      <td>2014-01-20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2014-01-23</td>\n",
       "      <td>9.263447</td>\n",
       "      <td>8.628803</td>\n",
       "      <td>9.852847</td>\n",
       "      <td>9.732818</td>\n",
       "      <td>2014-01-20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2014-01-24</td>\n",
       "      <td>9.277452</td>\n",
       "      <td>8.693226</td>\n",
       "      <td>9.897891</td>\n",
       "      <td>9.866460</td>\n",
       "      <td>2014-01-20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2014-01-25</td>\n",
       "      <td>9.087565</td>\n",
       "      <td>8.447306</td>\n",
       "      <td>9.728898</td>\n",
       "      <td>9.370927</td>\n",
       "      <td>2014-01-20</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          ds      yhat  yhat_lower  yhat_upper          y     cutoff\n",
       "0 2014-01-21  9.439510    8.799215   10.080240  10.542574 2014-01-20\n",
       "1 2014-01-22  9.267086    8.645900    9.882225  10.004283 2014-01-20\n",
       "2 2014-01-23  9.263447    8.628803    9.852847   9.732818 2014-01-20\n",
       "3 2014-01-24  9.277452    8.693226    9.897891   9.866460 2014-01-20\n",
       "4 2014-01-25  9.087565    8.447306    9.728898   9.370927 2014-01-20"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from fbprophet.diagnostics import cross_validation\n",
    "df_cv = cross_validation(m, horizon = '730 days')\n",
    "df_cv.head()"
   ]
  }
 ],
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