{ "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", "\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": { "image/png": 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", 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" ] }, "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([5.65805541, 5.3290277 , 5.16451385, 5.08225693, 5.04112846,\n", " 5.02056423, 5.01028212, 5.00514106, 5.00257053, 5.00128526])" ] }, "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: 0.992\n", "Mean Model: AR-X Adj. R-squared: 0.992\n", "Vol Model: GARCH Log-Likelihood: -1391.04\n", "Distribution: Normal AIC: 2796.08\n", "Method: Maximum Likelihood BIC: 2830.43\n", " No. Observations: 999\n", "Date: Tue, May 30 2023 Df Residuals: 995\n", "Time: 10:55:41 Df Model: 4\n", " Mean Model \n", "========================================================================\n", " coef std err t P>|t| 95.0% Conf. Int.\n", "------------------------------------------------------------------------\n", "Const 2.9447 0.151 19.443 3.308e-84 [ 2.648, 3.242]\n", "data[1] 0.6947 3.807e-03 182.482 0.000 [ 0.687, 0.702]\n", "x0 1.9813 2.175e-02 91.078 0.000 [ 1.939, 2.024]\n", "x1 -1.9620 2.564e-02 -76.519 0.000 [ -2.012, -1.912]\n", " Volatility Model \n", "==========================================================================\n", " coef std err t P>|t| 95.0% Conf. Int.\n", "--------------------------------------------------------------------------\n", "omega 0.0946 3.606e-02 2.622 8.733e-03 [2.389e-02, 0.165]\n", "alpha[1] 0.0974 2.496e-02 3.903 9.516e-05 [4.849e-02, 0.146]\n", "beta[1] 0.8083 5.059e-02 15.977 1.839e-57 [ 0.709, 0.907]\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": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "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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12.829543 12.241130 11.767149 \n", "995 8.954356 8.965773 9.025626 9.109140 \n", "996 9.034509 9.077894 9.148903 9.231197 \n", "997 11.722401 11.396828 11.121754 10.891488 \n", "998 11.016716 10.747264 10.542302 10.386034 \n", "999 9.902827 9.913039 9.918147 9.918574 " ] }, "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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", "text/plain": [ "
" ] }, "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": [ "0.0" ] }, "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", "
\n", "

WARNING

\n", " Other sizes are not allowed. The size of the out-of-sample data must either match the original data size or the number of forecasts.\n", "
" ] }, { "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": [ "0.0" ] }, "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: 0.955\n", "Mean Model: AR-X Adj. R-squared: 0.955\n", "Vol Model: GARCH Log-Likelihood: -2280.96\n", "Distribution: Normal AIC: 4573.92\n", "Method: Maximum Likelihood BIC: 4603.36\n", " No. Observations: 999\n", "Date: Tue, May 30 2023 Df Residuals: 996\n", "Time: 10:55:42 Df Model: 3\n", " Mean Model \n", "========================================================================\n", " coef std err t P>|t| 95.0% Conf. Int.\n", "------------------------------------------------------------------------\n", "Const -6.4609 0.226 -28.561 2.064e-179 [ -6.904, -6.018]\n", "data[1] 0.7695 8.995e-03 85.552 0.000 [ 0.752, 0.787]\n", "x0 1.7394 5.329e-02 32.643 1.021e-233 [ 1.635, 1.844]\n", " Volatility Model \n", "=============================================================================\n", " coef std err t P>|t| 95.0% Conf. Int.\n", "-----------------------------------------------------------------------------\n", "omega 0.1073 7.460e-02 1.438 0.150 [-3.895e-02, 0.253]\n", "alpha[1] 8.6689e-03 1.513e-02 0.573 0.567 [-2.099e-02,3.832e-02]\n", "beta[1] 0.9717 2.616e-02 37.149 4.549e-302 [ 0.920, 1.023]\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([[1.04095499, 1.27798546, 1.30149937, 1.53498654, 1.60825322,\n", " 1.53831759, 1.55948399, 1.49811376, 1.74794163, 1.54496175]])" ] }, "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([[2.95980851, 4.9043695 , 6.49587772, 7.50716786, 8.27211937,\n", " 8.71428305, 8.71321666, 8.67711577, 8.80764753, 9.17554847]])" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "joined = np.concatenate(simulations, 1)\n", "joined.std(1)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.11" } }, "nbformat": 4, "nbformat_minor": 4 }