{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# Forecasting with Exogenous Regressors\n",
    "\n",
    "This notebook provides examples of the accepted data structures for passing the expected value of exogenous variables when these are included in the mean.  For example, consider an AR(1) with 2 exogenous variables. The mean dynamics are\n",
    "\n",
    "$$ Y_t = \\phi_0 + \\phi_1 Y_{t-1} + \\beta_0 X_{0,t} + \\beta_1 X_{1,t} + \\epsilon_t. $$\n",
    "\n",
    "The $h$-step forecast, $E_{T}[Y_{t+h}]$, depends on the conditional expectation of $X_{0,T+h}$ and $X_{1,T+h}$,\n",
    "\n",
    "$$ E_{T}[Y_{T+h}] = \\phi_0 + \\phi_1 E_{T}[Y_{T+h-1}] + \\beta_0 E_{T}[X_{0,T+h}] +\\beta_1 E_{T}[X_{1,T+h}] $$\n",
    "\n",
    "where $E_{T}[Y_{T+h-1}]$ has been recursively computed.\n",
    "\n",
    "In order to construct forecasts up to some horizon $h$, it is necessary to pass $2\\times h$ values ($h$ for each series).  If using the features of `forecast` that allow many forecast to be specified, it necessary to supply $n \\times 2 \\times h$ values.\n",
    "\n",
    "There are two general purpose data structures that can be used for any number of exogenous variables and any number steps ahead:\n",
    "\n",
    "* `dict` - The values can be pass using a `dict` where the keys are the variable names and the values are 2-dimensional arrays. This is the most natural generalization of a pandas `DataFrame` to 3-dimensions.\n",
    "* `array` - The vales can alternatively be passed as a 3-d NumPy `array` where dimension 0 tracks the regressor index, dimension 1 is the time period and dimension 2 is the horizon.\n",
    "\n",
    "When a model contains a single exogenous regressor it is possible to use a 2-d array or `DataFrame` where dim0 tracks the time period where the forecast is generated and dimension 1 tracks the horizon.\n",
    "\n",
    "In the special case where a model contains a single regressor _and_ the horizon is 1, then a 1-d array of pandas Series can be used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# initial setup\n",
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn\n",
    "from arch.__future__ import reindexing\n",
    "\n",
    "seaborn.set_style(\"darkgrid\")\n",
    "plt.rc(\"figure\", figsize=(16, 6))\n",
    "plt.rc(\"savefig\", dpi=90)\n",
    "plt.rc(\"font\", family=\"sans-serif\")\n",
    "plt.rc(\"font\", size=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Simulating data\n",
    "\n",
    "Two $X$ variables are simulated and are assumed to follow independent AR(1) processes. The data is then assumed to follow an ARX(1) with 2 exogenous regressors and GARCH(1,1) errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "from arch.univariate import ARX, GARCH, ZeroMean, arch_model\n",
    "\n",
    "burn = 250\n",
    "\n",
    "x_mod = ARX(None, lags=1)\n",
    "x0 = x_mod.simulate([1, 0.8, 1], nobs=1000 + burn).data\n",
    "x1 = x_mod.simulate([2.5, 0.5, 1], nobs=1000 + burn).data\n",
    "\n",
    "resid_mod = ZeroMean(volatility=GARCH())\n",
    "resids = resid_mod.simulate([0.1, 0.1, 0.8], nobs=1000 + burn).data\n",
    "\n",
    "phi1 = 0.7\n",
    "phi0 = 3\n",
    "y = 10 + resids.copy()\n",
    "for i in range(1, y.shape[0]):\n",
    "    y[i] = phi0 + phi1 * y[i - 1] + 2 * x0[i] - 2 * x1[i] + resids[i]\n",
    "\n",
    "x0 = x0.iloc[-1000:]\n",
    "x1 = x1.iloc[-1000:]\n",
    "y = y.iloc[-1000:]\n",
    "y.index = x0.index = x1.index = np.arange(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Plotting the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = pd.DataFrame({\"ARX\": y}).plot(legend=False)\n",
    "ax.legend(frameon=False)\n",
    "_ = ax.set_xlim(0, 999)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Forecasting the X values\n",
    "\n",
    "The forecasts of $Y$ depend on forecasts of $X_0$ and $X_1$.  Both of these follow simple AR(1), and so we can construct the forecasts for all time horizons.  Note that the value in position `[i,j]` is the time-`i` forecast for horizon `j+1`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.32610653, 5.16305327, 5.08152663, 5.04076332, 5.02038166,\n",
       "       5.01019083, 5.00509541, 5.00254771, 5.00127385, 5.00063693])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0_oos = np.empty((1000, 10))\n",
    "x1_oos = np.empty((1000, 10))\n",
    "for i in range(10):\n",
    "    if i == 0:\n",
    "        last = x0\n",
    "    else:\n",
    "        last = x0_oos[:, i - 1]\n",
    "    x0_oos[:, i] = 1 + 0.8 * last\n",
    "    if i == 0:\n",
    "        last = x1\n",
    "    else:\n",
    "        last = x1_oos[:, i - 1]\n",
    "    x1_oos[:, i] = 2.5 + 0.5 * last\n",
    "\n",
    "x1_oos[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Fitting the model\n",
    "\n",
    "Next, the most is fit. The parameters are accurately estimated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                          AR-X - GARCH Model Results                          \n",
      "==============================================================================\n",
      "Dep. Variable:                   data   R-squared:                       0.993\n",
      "Mean Model:                      AR-X   Adj. R-squared:                  0.993\n",
      "Vol Model:                      GARCH   Log-Likelihood:               -1302.15\n",
      "Distribution:                  Normal   AIC:                           2618.31\n",
      "Method:            Maximum Likelihood   BIC:                           2652.65\n",
      "                                        No. Observations:                  999\n",
      "Date:                Mon, May 17 2021   Df Residuals:                      995\n",
      "Time:                        16:04:11   Df Model:                            4\n",
      "                               Mean Model                               \n",
      "========================================================================\n",
      "                 coef    std err          t      P>|t|  95.0% Conf. Int.\n",
      "------------------------------------------------------------------------\n",
      "Const          2.9480      0.149     19.818  2.088e-87 [  2.656,  3.240]\n",
      "data[1]        0.6971  3.421e-03    203.759      0.000 [  0.690,  0.704]\n",
      "x0             2.0186  2.063e-02     97.827      0.000 [  1.978,  2.059]\n",
      "x1            -2.0115  2.483e-02    -81.001      0.000 [ -2.060, -1.963]\n",
      "                              Volatility Model                             \n",
      "===========================================================================\n",
      "                 coef    std err          t      P>|t|     95.0% Conf. Int.\n",
      "---------------------------------------------------------------------------\n",
      "omega          0.1144  5.879e-02      1.946  5.162e-02 [-8.041e-04,  0.230]\n",
      "alpha[1]       0.0633  2.982e-02      2.123  3.374e-02  [4.866e-03,  0.122]\n",
      "beta[1]        0.7940  9.035e-02      8.788  1.522e-18    [  0.617,  0.971]\n",
      "===========================================================================\n",
      "\n",
      "Covariance estimator: robust\n"
     ]
    }
   ],
   "source": [
    "exog = pd.DataFrame({\"x0\": x0, \"x1\": x1})\n",
    "mod = arch_model(y, x=exog, mean=\"ARX\", lags=1)\n",
    "res = mod.fit(disp=\"off\")\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Using a `dict`\n",
    "\n",
    "The first approach uses a dict to pass the two variables. The key consideration here is the the keys of the dictionary must **exactly** match the variable names (`x0` and `x1` here).  The dictionary here contains only the final row of the forecast values since `forecast` will only make forecasts beginning from the final in-sample observation by default.\n",
    "\n",
    "### Using `DataFrame`\n",
    "\n",
    "While these examples make use of NumPy arrays, these can be `DataFrames`. This allows the index to be used to track the forecast origination point, which can be a helpful device."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "exog_fcast = {\"x0\": x0_oos[-1:], \"x1\": x1_oos[-1:]}\n",
    "forecasts = res.forecast(horizon=10, x=exog_fcast)\n",
    "forecasts.mean.T.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using an `array`\n",
    "\n",
    "An array can alternatively be used.  This frees the restriction on matching the variable names although the order must match instead. The forecast values are 2 (variables) by 1 (forecast) by 10 (horizon)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The shape is (2, 1, 10)\n",
      "     h.01  h.02  h.03  h.04  h.05  h.06  h.07  h.08  h.09  h.10\n",
      "999   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0\n"
     ]
    }
   ],
   "source": [
    "exog_fcast = np.array([x0_oos[-1:], x1_oos[-1:]])\n",
    "print(f\"The shape is {exog_fcast.shape}\")\n",
    "array_forecasts = res.forecast(horizon=10, x=exog_fcast)\n",
    "print(array_forecasts.mean - forecasts.mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Producing multiple forecasts\n",
    "\n",
    "`forecast` can produce multiple forecasts using the same fit model.  Here the model is fit to the first 500 observations and then forecasting for the remaining values are produced. It must be the case that the `x` values passed for `forecast` have the same number of rows as the table of forecasts produced.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>h.01</th>\n",
       "      <th>h.02</th>\n",
       "      <th>h.03</th>\n",
       "      <th>h.04</th>\n",
       "      <th>h.05</th>\n",
       "      <th>h.06</th>\n",
       "      <th>h.07</th>\n",
       "      <th>h.08</th>\n",
       "      <th>h.09</th>\n",
       "      <th>h.10</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>990</th>\n",
       "      <td>0.197255</td>\n",
       "      <td>0.766334</td>\n",
       "      <td>1.577107</td>\n",
       "      <td>2.505601</td>\n",
       "      <td>3.459461</td>\n",
       "      <td>4.377620</td>\n",
       "      <td>5.224185</td>\n",
       "      <td>5.981486</td>\n",
       "      <td>6.644090</td>\n",
       "      <td>7.214210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>991</th>\n",
       "      <td>-1.890108</td>\n",
       "      <td>-1.296009</td>\n",
       "      <td>-0.321045</td>\n",
       "      <td>0.826688</td>\n",
       "      <td>2.010886</td>\n",
       "      <td>3.148451</td>\n",
       "      <td>4.193448</td>\n",
       "      <td>5.124665</td>\n",
       "      <td>5.936575</td>\n",
       "      <td>6.633031</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>992</th>\n",
       "      <td>-8.507089</td>\n",
       "      <td>-7.755860</td>\n",
       "      <td>-6.044790</td>\n",
       "      <td>-4.011246</td>\n",
       "      <td>-1.975703</td>\n",
       "      <td>-0.089727</td>\n",
       "      <td>1.584868</td>\n",
       "      <td>3.033252</td>\n",
       "      <td>4.264283</td>\n",
       "      <td>5.297785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>993</th>\n",
       "      <td>-12.095946</td>\n",
       "      <td>-10.869621</td>\n",
       "      <td>-8.890602</td>\n",
       "      <td>-6.627904</td>\n",
       "      <td>-4.352285</td>\n",
       "      <td>-2.211499</td>\n",
       "      <td>-0.277740</td>\n",
       "      <td>1.422307</td>\n",
       "      <td>2.888448</td>\n",
       "      <td>4.135017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>994</th>\n",
       "      <td>-10.415586</td>\n",
       "      <td>-8.143577</td>\n",
       "      <td>-5.654791</td>\n",
       "      <td>-3.258179</td>\n",
       "      <td>-1.089347</td>\n",
       "      <td>0.805444</td>\n",
       "      <td>2.424787</td>\n",
       "      <td>3.788488</td>\n",
       "      <td>4.925033</td>\n",
       "      <td>5.865051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>995</th>\n",
       "      <td>-1.921109</td>\n",
       "      <td>1.075917</td>\n",
       "      <td>3.299730</td>\n",
       "      <td>4.950490</td>\n",
       "      <td>6.178127</td>\n",
       "      <td>7.093677</td>\n",
       "      <td>7.778853</td>\n",
       "      <td>8.293623</td>\n",
       "      <td>8.681971</td>\n",
       "      <td>8.976192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>996</th>\n",
       "      <td>-0.935776</td>\n",
       "      <td>1.954178</td>\n",
       "      <td>4.178160</td>\n",
       "      <td>5.832262</td>\n",
       "      <td>7.036522</td>\n",
       "      <td>7.901080</td>\n",
       "      <td>8.515904</td>\n",
       "      <td>8.950270</td>\n",
       "      <td>9.255725</td>\n",
       "      <td>9.469814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>997</th>\n",
       "      <td>2.416878</td>\n",
       "      <td>4.689798</td>\n",
       "      <td>6.409599</td>\n",
       "      <td>7.650164</td>\n",
       "      <td>8.515074</td>\n",
       "      <td>9.101508</td>\n",
       "      <td>9.488851</td>\n",
       "      <td>9.737583</td>\n",
       "      <td>9.891902</td>\n",
       "      <td>9.983206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>998</th>\n",
       "      <td>4.633381</td>\n",
       "      <td>6.555164</td>\n",
       "      <td>8.072909</td>\n",
       "      <td>9.153335</td>\n",
       "      <td>9.864477</td>\n",
       "      <td>10.296675</td>\n",
       "      <td>10.532205</td>\n",
       "      <td>10.636352</td>\n",
       "      <td>10.657221</td>\n",
       "      <td>10.628546</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>999</th>\n",
       "      <td>10.573900</td>\n",
       "      <td>12.317818</td>\n",
       "      <td>13.245648</td>\n",
       "      <td>13.612879</td>\n",
       "      <td>13.620680</td>\n",
       "      <td>13.415346</td>\n",
       "      <td>13.097526</td>\n",
       "      <td>12.733225</td>\n",
       "      <td>12.363590</td>\n",
       "      <td>12.012647</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          h.01       h.02       h.03       h.04       h.05       h.06  \\\n",
       "990   0.197255   0.766334   1.577107   2.505601   3.459461   4.377620   \n",
       "991  -1.890108  -1.296009  -0.321045   0.826688   2.010886   3.148451   \n",
       "992  -8.507089  -7.755860  -6.044790  -4.011246  -1.975703  -0.089727   \n",
       "993 -12.095946 -10.869621  -8.890602  -6.627904  -4.352285  -2.211499   \n",
       "994 -10.415586  -8.143577  -5.654791  -3.258179  -1.089347   0.805444   \n",
       "995  -1.921109   1.075917   3.299730   4.950490   6.178127   7.093677   \n",
       "996  -0.935776   1.954178   4.178160   5.832262   7.036522   7.901080   \n",
       "997   2.416878   4.689798   6.409599   7.650164   8.515074   9.101508   \n",
       "998   4.633381   6.555164   8.072909   9.153335   9.864477  10.296675   \n",
       "999  10.573900  12.317818  13.245648  13.612879  13.620680  13.415346   \n",
       "\n",
       "          h.07       h.08       h.09       h.10  \n",
       "990   5.224185   5.981486   6.644090   7.214210  \n",
       "991   4.193448   5.124665   5.936575   6.633031  \n",
       "992   1.584868   3.033252   4.264283   5.297785  \n",
       "993  -0.277740   1.422307   2.888448   4.135017  \n",
       "994   2.424787   3.788488   4.925033   5.865051  \n",
       "995   7.778853   8.293623   8.681971   8.976192  \n",
       "996   8.515904   8.950270   9.255725   9.469814  \n",
       "997   9.488851   9.737583   9.891902   9.983206  \n",
       "998  10.532205  10.636352  10.657221  10.628546  \n",
       "999  13.097526  12.733225  12.363590  12.012647  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res = mod.fit(disp=\"off\", last_obs=500)\n",
    "exog_fcast = {\"x0\": x0_oos[-500:], \"x1\": x1_oos[-500:]}\n",
    "multi_forecasts = res.forecast(start=500, horizon=10, x=exog_fcast)\n",
    "multi_forecasts.mean.tail(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plot of the final 5 forecast paths shows the the mean reversion of the process."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = multi_forecasts.mean.tail().T.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The previous example made use of dictionaries where each of the values was a 500 (number of forecasts) by 10 (horizon) array.  The alternative format can be used where `x` is a 3-d array with shape 2 (variables) by 500 (forecasts) by 10 (horizon)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 500, 10)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "h.01    0.0\n",
       "h.02    0.0\n",
       "h.03    0.0\n",
       "h.04    0.0\n",
       "h.05    0.0\n",
       "h.06    0.0\n",
       "h.07    0.0\n",
       "h.08    0.0\n",
       "h.09    0.0\n",
       "h.10    0.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exog_fcast = np.array([x0_oos[-500:], x1_oos[-500:]])\n",
    "print(exog_fcast.shape)\n",
    "array_multi_forecasts = res.forecast(start=500, horizon=10, x=exog_fcast)\n",
    "np.max(np.abs(array_multi_forecasts.mean - multi_forecasts.mean))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## `x` input array sizes\n",
    "\n",
    "While the natural shape of the `x` data is the number of forecasts, it is also possible to pass an `x` that has the same shape as the `y` used to construct the model.  The may simplify tracking the origin points of the forecast.  Values are are not needed are ignored. In this example, the out-of-sample values are 2 by 1000 (original number of observations) by 10.  Only the final 500 are used. \n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "    <h3><b>WARNING</b></h3>\n",
    "    Other sizes are <b>not</b> allowed. The size of the out-of-sample data must either match the original data size or the number of forecasts.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 1000, 10)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "h.01    0.0\n",
       "h.02    0.0\n",
       "h.03    0.0\n",
       "h.04    0.0\n",
       "h.05    0.0\n",
       "h.06    0.0\n",
       "h.07    0.0\n",
       "h.08    0.0\n",
       "h.09    0.0\n",
       "h.10    0.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exog_fcast = np.array([x0_oos, x1_oos])\n",
    "print(exog_fcast.shape)\n",
    "array_multi_forecasts = res.forecast(start=500, horizon=10, x=exog_fcast)\n",
    "np.max(np.abs(array_multi_forecasts.mean - multi_forecasts.mean))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Special Cases with a single `x` variable\n",
    "\n",
    "When a model consists of a single exogenous regressor, then `x` can be a 1-d or 2-d array (or `Series` or `DataFrame`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                          AR-X - GARCH Model Results                          \n",
      "==============================================================================\n",
      "Dep. Variable:                   data   R-squared:                       0.949\n",
      "Mean Model:                      AR-X   Adj. R-squared:                  0.949\n",
      "Vol Model:                      GARCH   Log-Likelihood:               -2310.31\n",
      "Distribution:                  Normal   AIC:                           4632.63\n",
      "Method:            Maximum Likelihood   BIC:                           4662.07\n",
      "                                        No. Observations:                  999\n",
      "Date:                Mon, May 17 2021   Df Residuals:                      996\n",
      "Time:                        16:04:11   Df Model:                            3\n",
      "                               Mean Model                               \n",
      "========================================================================\n",
      "                 coef    std err          t      P>|t|  95.0% Conf. Int.\n",
      "------------------------------------------------------------------------\n",
      "Const         -6.3468      0.283    -22.464 9.346e-112 [ -6.901, -5.793]\n",
      "data[1]        0.7555  9.631e-03     78.446      0.000 [  0.737,  0.774]\n",
      "x0             1.7840  6.195e-02     28.799 2.192e-182 [  1.663,  1.905]\n",
      "                             Volatility Model                             \n",
      "==========================================================================\n",
      "                 coef    std err          t      P>|t|    95.0% Conf. Int.\n",
      "--------------------------------------------------------------------------\n",
      "omega          3.0493      0.753      4.052  5.085e-05   [  1.574,  4.524]\n",
      "alpha[1]       0.1626  3.741e-02      4.346  1.385e-05 [8.926e-02,  0.236]\n",
      "beta[1]        0.3401      0.129      2.631  8.523e-03 [8.670e-02,  0.593]\n",
      "==========================================================================\n",
      "\n",
      "Covariance estimator: robust\n"
     ]
    }
   ],
   "source": [
    "mod = arch_model(y, x=exog.iloc[:, :1], mean=\"ARX\", lags=1)\n",
    "res = mod.fit(disp=\"off\")\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These two examples show that both formats can be used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     h.01  h.02  h.03  h.04  h.05  h.06  h.07  h.08  h.09  h.10\n",
      "999   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0   0.0\n"
     ]
    }
   ],
   "source": [
    "forecast_1d = res.forecast(horizon=10, x=x0_oos[-1])\n",
    "forecast_2d = res.forecast(horizon=10, x=x0_oos[-1:])\n",
    "print(forecast_1d.mean - forecast_2d.mean)\n",
    "\n",
    "## Simulation-forecasting\n",
    "\n",
    "mod = arch_model(y, x=exog, mean=\"ARX\", lags=1, power=1.0)\n",
    "res = mod.fit(disp=\"off\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation\n",
    "\n",
    "`forecast` supports simulating paths. When forecasting a model with exogenous variables, the same value is used to in all mean paths.  If you wish to also simulate the paths of the `x` variables, these need to generated and then passed inside a loop. \n",
    "\n",
    "### Static out-of-sample `x`\n",
    "This first example shows that variance of the paths when the same `x` values are used in the forecast. There is a sense the out-of-sample `x` are treated as deterministic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.94510757, 0.97700028, 1.13035701, 1.10824845, 1.26825095,\n",
       "        1.26590793, 1.23342443, 1.18098812, 1.28265677, 1.2315994 ]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = {\"x0\": x0_oos[-1], \"x1\": x1_oos[-1]}\n",
    "sim_fixedx = res.forecast(horizon=10, x=x, method=\"simulation\", simulations=100)\n",
    "sim_fixedx.simulations.values.std(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Simulating the out-of-sample `x`\n",
    "\n",
    "This example simulates distinct paths for the two exogenous variables and then simulates a single path.  This is then repeated 100 times.  We see that variance is much higher when we account for variation in the x data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "from numpy.random import RandomState\n",
    "\n",
    "\n",
    "def sim_ar1(params: np.ndarray, initial: float, horizon: int, rng: RandomState):\n",
    "    out = np.zeros(horizon)\n",
    "    shocks = rng.standard_normal(horizon)\n",
    "    out[0] = params[0] + params[1] * initial + shocks[0]\n",
    "    for i in range(1, horizon):\n",
    "        out[i] = params[0] + params[1] * out[i - 1] + shocks[i]\n",
    "    return out\n",
    "\n",
    "\n",
    "simulations = []\n",
    "rng = RandomState(20210301)\n",
    "for i in range(100):\n",
    "    x0_sim = sim_ar1(np.array([1, 0.8]), x0.iloc[-1], 10, rng)\n",
    "    x1_sim = sim_ar1(np.array([2.5, 0.5]), x1.iloc[-1], 10, rng)\n",
    "    x = {\"x0\": x0_sim, \"x1\": x1_sim}\n",
    "    fcast = res.forecast(horizon=10, x=x, method=\"simulation\", simulations=1)\n",
    "    simulations.append(fcast.simulations.values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally the standard deviation is quite a bit larger. This is a most accurate value fo the long-run variance of the forecast residuals which should account for dynamics in the model and any exogenous regressors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3.21343234, 4.99297815, 6.29477322, 7.49884207, 8.47501636,\n",
       "        8.64628226, 8.72478144, 8.78606273, 9.03824963, 9.30368669]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "joined = np.concatenate(simulations, 1)\n",
    "joined.std(1)"
   ]
  }
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