{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Prediction (out of sample)" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:39:38.366238Z", "iopub.status.busy": "2023-12-14T14:39:38.365784Z", "iopub.status.idle": "2023-12-14T14:39:39.436056Z", "shell.execute_reply": "2023-12-14T14:39:39.435150Z" } }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:39:39.441690Z", "iopub.status.busy": "2023-12-14T14:39:39.440188Z", "iopub.status.idle": "2023-12-14T14:39:40.659007Z", "shell.execute_reply": "2023-12-14T14:39:40.658011Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "import statsmodels.api as sm\n", "\n", "plt.rc(\"figure\", figsize=(16, 8))\n", "plt.rc(\"font\", size=14)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Artificial data" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:39:40.663039Z", "iopub.status.busy": "2023-12-14T14:39:40.662639Z", "iopub.status.idle": "2023-12-14T14:39:40.669832Z", "shell.execute_reply": "2023-12-14T14:39:40.669018Z" } }, "outputs": [], "source": [ "nsample = 50\n", "sig = 0.25\n", "x1 = np.linspace(0, 20, nsample)\n", "X = np.column_stack((x1, np.sin(x1), (x1 - 5) ** 2))\n", "X = sm.add_constant(X)\n", "beta = [5.0, 0.5, 0.5, -0.02]\n", "y_true = np.dot(X, beta)\n", "y = y_true + sig * np.random.normal(size=nsample)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Estimation " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:39:40.673207Z", "iopub.status.busy": "2023-12-14T14:39:40.672810Z", "iopub.status.idle": "2023-12-14T14:39:40.690855Z", "shell.execute_reply": "2023-12-14T14:39:40.690107Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: y R-squared: 0.985\n", "Model: OLS Adj. R-squared: 0.984\n", "Method: Least Squares F-statistic: 1018.\n", "Date: Thu, 14 Dec 2023 Prob (F-statistic): 4.80e-42\n", "Time: 14:39:40 Log-Likelihood: 3.0746\n", "No. Observations: 50 AIC: 1.851\n", "Df Residuals: 46 BIC: 9.499\n", "Df Model: 3 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const 4.9317 0.081 60.993 0.000 4.769 5.094\n", "x1 0.5066 0.012 40.625 0.000 0.482 0.532\n", "x2 0.5504 0.049 11.227 0.000 0.452 0.649\n", "x3 -0.0206 0.001 -18.810 0.000 -0.023 -0.018\n", "==============================================================================\n", "Omnibus: 2.839 Durbin-Watson: 2.081\n", "Prob(Omnibus): 0.242 Jarque-Bera (JB): 2.094\n", "Skew: -0.492 Prob(JB): 0.351\n", "Kurtosis: 3.190 Cond. No. 221.\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" ] } ], "source": [ "olsmod = sm.OLS(y, X)\n", "olsres = olsmod.fit()\n", "print(olsres.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## In-sample prediction" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:39:40.782977Z", "iopub.status.busy": "2023-12-14T14:39:40.782621Z", "iopub.status.idle": "2023-12-14T14:39:40.787813Z", "shell.execute_reply": "2023-12-14T14:39:40.787046Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 4.41682151 4.92268515 5.38579485 5.77615583 6.07459828 6.27592688\n", " 6.38977441 6.43901906 6.45602567 6.47732824 6.53762749 6.66408968\n", " 6.8718832 7.1616865 7.51957661 7.91931663 8.32666638 8.705008\n", " 9.02136211 9.25180625 9.3854053 9.42600804 9.39161484 9.31142024\n", " 9.22101636 9.15654525 9.14876081 9.21797603 9.37072562 9.59869241\n", " 9.88007377 10.18316377 10.47156237 10.71015582 10.87088578 10.9373592\n", " 10.90754167 10.79409166 10.62228076 10.42584165 10.2414259 10.10258223\n", " 10.03424454 10.04863535 10.14325767 10.30130525 10.49442381 10.68736953\n", " 10.84379957 10.93224304]\n" ] } ], "source": [ "ypred = olsres.predict(X)\n", "print(ypred)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Create a new sample of explanatory variables Xnew, predict and plot" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:39:40.790712Z", "iopub.status.busy": "2023-12-14T14:39:40.790187Z", "iopub.status.idle": "2023-12-14T14:39:40.795393Z", "shell.execute_reply": "2023-12-14T14:39:40.794565Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[10.91763232 10.75840089 10.47613227 10.12001251 9.75478779 9.44491225\n", " 9.23876741 9.15681664 9.18659505 9.28576134]\n" ] } ], "source": [ "x1n = np.linspace(20.5, 25, 10)\n", "Xnew = np.column_stack((x1n, np.sin(x1n), (x1n - 5) ** 2))\n", "Xnew = sm.add_constant(Xnew)\n", "ynewpred = olsres.predict(Xnew) # predict out of sample\n", "print(ynewpred)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot comparison" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:39:40.798070Z", "iopub.status.busy": "2023-12-14T14:39:40.797744Z", "iopub.status.idle": "2023-12-14T14:39:41.087194Z", "shell.execute_reply": "2023-12-14T14:39:41.086371Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(x1, y, \"o\", label=\"Data\")\n", "ax.plot(x1, y_true, \"b-\", label=\"True\")\n", "ax.plot(np.hstack((x1, x1n)), np.hstack((ypred, ynewpred)), \"r\", label=\"OLS prediction\")\n", "ax.legend(loc=\"best\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Predicting with Formulas" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using formulas can make both estimation and prediction a lot easier" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:39:41.090551Z", "iopub.status.busy": "2023-12-14T14:39:41.090071Z", "iopub.status.idle": "2023-12-14T14:39:41.097714Z", "shell.execute_reply": "2023-12-14T14:39:41.097139Z" } }, "outputs": [], "source": [ "from statsmodels.formula.api import ols\n", "\n", "data = {\"x1\": x1, \"y\": y}\n", "\n", "res = ols(\"y ~ x1 + np.sin(x1) + I((x1-5)**2)\", data=data).fit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the `I` to indicate use of the Identity transform. Ie., we do not want any expansion magic from using `**2`" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:39:41.100558Z", "iopub.status.busy": "2023-12-14T14:39:41.100203Z", "iopub.status.idle": "2023-12-14T14:39:41.106958Z", "shell.execute_reply": "2023-12-14T14:39:41.105858Z" } }, "outputs": [ { "data": { "text/plain": [ "Intercept 4.931706\n", "x1 0.506602\n", "np.sin(x1) 0.550372\n", "I((x1 - 5) ** 2) -0.020595\n", "dtype: float64" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res.params" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we only have to pass the single variable and we get the transformed right-hand side variables automatically" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2023-12-14T14:39:41.110438Z", "iopub.status.busy": "2023-12-14T14:39:41.109890Z", "iopub.status.idle": "2023-12-14T14:39:41.117999Z", "shell.execute_reply": "2023-12-14T14:39:41.117381Z" } }, "outputs": [ { "data": { "text/plain": [ "0 10.917632\n", "1 10.758401\n", "2 10.476132\n", "3 10.120013\n", "4 9.754788\n", "5 9.444912\n", "6 9.238767\n", "7 9.156817\n", "8 9.186595\n", "9 9.285761\n", "dtype: float64" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "res.predict(exog=dict(x1=x1n))" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 4 }