{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# SARIMAX: Model selection, missing data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The example mirrors Durbin and Koopman (2012), Chapter 8.4 in application of Box-Jenkins methodology to fit ARMA models. The novel feature is the ability of the model to work on datasets with missing values." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2021-02-02T07:05:17.899232Z", "iopub.status.busy": "2021-02-02T07:05:17.898401Z", "iopub.status.idle": "2021-02-02T07:05:19.047440Z", "shell.execute_reply": "2021-02-02T07:05:19.048747Z" } }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2021-02-02T07:05:19.053914Z", "iopub.status.busy": "2021-02-02T07:05:19.052441Z", "iopub.status.idle": "2021-02-02T07:05:21.739096Z", "shell.execute_reply": "2021-02-02T07:05:21.740381Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "from scipy.stats import norm\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2021-02-02T07:05:21.745721Z", "iopub.status.busy": "2021-02-02T07:05:21.744176Z", "iopub.status.idle": "2021-02-02T07:05:22.679505Z", "shell.execute_reply": "2021-02-02T07:05:22.680235Z" } }, "outputs": [], "source": [ "import requests\n", "from io import BytesIO\n", "from zipfile import ZipFile\n", "\n", "# Download the dataset\n", "dk = requests.get('http://www.ssfpack.com/files/DK-data.zip').content\n", "f = BytesIO(dk)\n", "zipped = ZipFile(f)\n", "df = pd.read_table(\n", " BytesIO(zipped.read('internet.dat')),\n", " skiprows=1, header=None, sep='\\s+', engine='python',\n", " names=['internet','dinternet']\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Model Selection\n", "\n", "As in Durbin and Koopman, we force a number of the values to be missing." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2021-02-02T07:05:22.687575Z", "iopub.status.busy": "2021-02-02T07:05:22.686568Z", "iopub.status.idle": "2021-02-02T07:05:22.695011Z", "shell.execute_reply": "2021-02-02T07:05:22.696650Z" } }, "outputs": [], "source": [ "# Get the basic series\n", "dta_full = df.dinternet[1:].values\n", "dta_miss = dta_full.copy()\n", "\n", "# Remove datapoints\n", "missing = np.r_[6,16,26,36,46,56,66,72,73,74,75,76,86,96]-1\n", "dta_miss[missing] = np.nan" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then we can consider model selection using the Akaike information criteria (AIC), but running the model for each variant and selecting the model with the lowest AIC value.\n", "\n", "There are a couple of things to note here:\n", "\n", "- When running such a large batch of models, particularly when the autoregressive and moving average orders become large, there is the possibility of poor maximum likelihood convergence. Below we ignore the warnings since this example is illustrative.\n", "- We use the option `enforce_invertibility=False`, which allows the moving average polynomial to be non-invertible, so that more of the models are estimable.\n", "- Several of the models do not produce good results, and their AIC value is set to NaN. This is not surprising, as Durbin and Koopman note numerical problems with the high order models." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2021-02-02T07:05:22.708489Z", "iopub.status.busy": "2021-02-02T07:05:22.707667Z", "iopub.status.idle": "2021-02-02T07:05:47.791488Z", "shell.execute_reply": "2021-02-02T07:05:47.792705Z" } }, "outputs": [], "source": [ "import warnings\n", "\n", "aic_full = pd.DataFrame(np.zeros((6,6), dtype=float))\n", "aic_miss = pd.DataFrame(np.zeros((6,6), dtype=float))\n", "\n", "warnings.simplefilter('ignore')\n", "\n", "# Iterate over all ARMA(p,q) models with p,q in [0,6]\n", "for p in range(6):\n", " for q in range(6):\n", " if p == 0 and q == 0:\n", " continue\n", " \n", " # Estimate the model with no missing datapoints\n", " mod = sm.tsa.statespace.SARIMAX(dta_full, order=(p,0,q), enforce_invertibility=False)\n", " try:\n", " res = mod.fit(disp=False)\n", " aic_full.iloc[p,q] = res.aic\n", " except:\n", " aic_full.iloc[p,q] = np.nan\n", " \n", " # Estimate the model with missing datapoints\n", " mod = sm.tsa.statespace.SARIMAX(dta_miss, order=(p,0,q), enforce_invertibility=False)\n", " try:\n", " res = mod.fit(disp=False)\n", " aic_miss.iloc[p,q] = res.aic\n", " except:\n", " aic_miss.iloc[p,q] = np.nan" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the models estimated over the full (non-missing) dataset, the AIC chooses ARMA(1,1) or ARMA(3,0). Durbin and Koopman suggest the ARMA(1,1) specification is better due to parsimony.\n", "\n", "$$\n", "\\text{Replication of:}\\\\\n", "\\textbf{Table 8.1} ~~ \\text{AIC for different ARMA models.}\\\\\n", "\\newcommand{\\r}[1]{{\\color{red}{#1}}}\n", "\\begin{array}{lrrrrrr}\n", "\\hline\n", "q & 0 & 1 & 2 & 3 & 4 & 5 \\\\\n", "\\hline\n", "p & {} & {} & {} & {} & {} & {} \\\\\n", "0 & 0.00 & 549.81 & 519.87 & 520.27 & 519.38 & 518.86 \\\\\n", "1 & 529.24 & \\r{514.30} & 516.25 & 514.58 & 515.10 & 516.28 \\\\\n", "2 & 522.18 & 516.29 & 517.16 & 515.77 & 513.24 & 514.73 \\\\\n", "3 & \\r{511.99} & 513.94 & 515.92 & 512.06 & 513.72 & 514.50 \\\\\n", "4 & 513.93 & 512.89 & nan & nan & 514.81 & 516.08 \\\\\n", "5 & 515.86 & 517.64 & nan & nan & nan & nan \\\\\n", "\\hline\n", "\\end{array}\n", "$$\n", "\n", "For the models estimated over missing dataset, the AIC chooses ARMA(1,1)\n", "\n", "$$\n", "\\text{Replication of:}\\\\\n", "\\textbf{Table 8.2} ~~ \\text{AIC for different ARMA models with missing observations.}\\\\\n", "\\begin{array}{lrrrrrr}\n", "\\hline\n", "q & 0 & 1 & 2 & 3 & 4 & 5 \\\\\n", "\\hline\n", "p & {} & {} & {} & {} & {} & {} \\\\\n", "0 & 0.00 & 488.93 & 464.01 & 463.86 & 462.63 & 463.62 \\\\\n", "1 & 468.01 & \\r{457.54} & 459.35 & 458.66 & 459.15 & 461.01 \\\\\n", "2 & 469.68 & nan & 460.48 & 459.43 & 459.23 & 460.47 \\\\\n", "3 & 467.10 & 458.44 & 459.64 & 456.66 & 459.54 & 460.05 \\\\\n", "4 & 469.00 & 459.52 & nan & 463.04 & 459.35 & 460.96 \\\\\n", "5 & 471.32 & 461.26 & nan & nan & 461.00 & 462.97 \\\\\n", "\\hline\n", "\\end{array}\n", "$$\n", "\n", "**Note**: the AIC values are calculated differently than in Durbin and Koopman, but show overall similar trends." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Postestimation\n", "\n", "Using the ARMA(1,1) specification selected above, we perform in-sample prediction and out-of-sample forecasting." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2021-02-02T07:05:47.797852Z", "iopub.status.busy": "2021-02-02T07:05:47.796351Z", "iopub.status.idle": "2021-02-02T07:05:47.862084Z", "shell.execute_reply": "2021-02-02T07:05:47.863137Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " SARIMAX Results \n", "==============================================================================\n", "Dep. Variable: y No. Observations: 99\n", "Model: SARIMAX(1, 0, 1) Log Likelihood -225.770\n", "Date: Tue, 02 Feb 2021 AIC 457.541\n", "Time: 07:05:47 BIC 465.326\n", "Sample: 0 HQIC 460.691\n", " - 99 \n", "Covariance Type: opg \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "ar.L1 0.6562 0.092 7.125 0.000 0.476 0.837\n", "ma.L1 0.4878 0.111 4.390 0.000 0.270 0.706\n", "sigma2 10.3402 1.569 6.591 0.000 7.265 13.415\n", "===================================================================================\n", "Ljung-Box (L1) (Q): 0.00 Jarque-Bera (JB): 1.87\n", "Prob(Q): 0.96 Prob(JB): 0.39\n", "Heteroskedasticity (H): 0.59 Skew: -0.10\n", "Prob(H) (two-sided): 0.13 Kurtosis: 3.64\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n" ] } ], "source": [ "# Statespace\n", "mod = sm.tsa.statespace.SARIMAX(dta_miss, order=(1,0,1))\n", "res = mod.fit(disp=False)\n", "print(res.summary())" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "execution": { "iopub.execute_input": "2021-02-02T07:05:47.868071Z", "iopub.status.busy": "2021-02-02T07:05:47.866563Z", "iopub.status.idle": "2021-02-02T07:05:48.132098Z", "shell.execute_reply": "2021-02-02T07:05:48.130960Z" } }, "outputs": [ { "data": { "text/plain": [ "[Text(0.5, 1.0, 'Figure 8.9 - Internet series')]" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# In-sample one-step-ahead predictions, and out-of-sample forecasts\n", "nforecast = 20\n", "predict = res.get_prediction(end=mod.nobs + nforecast)\n", "idx = np.arange(len(predict.predicted_mean))\n", "predict_ci = predict.conf_int(alpha=0.5)\n", "\n", "# Graph\n", "fig, ax = plt.subplots(figsize=(12,6))\n", "ax.xaxis.grid()\n", "ax.plot(dta_miss, 'k.')\n", "\n", "# Plot\n", "ax.plot(idx[:-nforecast], predict.predicted_mean[:-nforecast], 'gray')\n", "ax.plot(idx[-nforecast:], predict.predicted_mean[-nforecast:], 'k--', linestyle='--', linewidth=2)\n", "ax.fill_between(idx, predict_ci[:, 0], predict_ci[:, 1], alpha=0.15)\n", "\n", "ax.set(title='Figure 8.9 - Internet series');" ] } ], "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": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 0 }