{ "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 }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "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 }, "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 }, "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 }, "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 }, "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, 17 Dec 2019 AIC 457.541\n", "Time: 23:41:53 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 (Q): 36.52 Jarque-Bera (JB): 1.87\n", "Prob(Q): 0.63 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 }, "outputs": [ { "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": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 0 }