{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# SARIMAX: Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This notebook replicates examples from the Stata ARIMA time series estimation and postestimation documentation.\n", "\n", "First, we replicate the four estimation examples http://www.stata.com/manuals13/tsarima.pdf:\n", "\n", "1. ARIMA(1,1,1) model on the U.S. Wholesale Price Index (WPI) dataset.\n", "2. Variation of example 1 which adds an MA(4) term to the ARIMA(1,1,1) specification to allow for an additive seasonal effect.\n", "3. ARIMA(2,1,0) x (1,1,0,12) model of monthly airline data. This example allows a multiplicative seasonal effect.\n", "4. ARMA(1,1) model with exogenous regressors; describes consumption as an autoregressive process on which also the money supply is assumed to be an explanatory variable.\n", "\n", "Second, we demonstrate postestimation capabilities to replicate http://www.stata.com/manuals13/tsarimapostestimation.pdf. The model from example 4 is used to demonstrate:\n", "\n", "1. One-step-ahead in-sample prediction\n", "2. n-step-ahead out-of-sample forecasting\n", "3. n-step-ahead in-sample dynamic prediction" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "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\n", "from datetime import datetime\n", "import requests\n", "from io import BytesIO\n", "# Register converters to avoid warnings\n", "pd.plotting.register_matplotlib_converters()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ARIMA Example 1: Arima\n", "\n", "As can be seen in the graphs from Example 2, the Wholesale price index (WPI) is growing over time (i.e. is not stationary). Therefore an ARMA model is not a good specification. In this first example, we consider a model where the original time series is assumed to be integrated of order 1, so that the difference is assumed to be stationary, and fit a model with one autoregressive lag and one moving average lag, as well as an intercept term.\n", "\n", "The postulated data process is then:\n", "\n", "$$\n", "\\Delta y_t = c + \\phi_1 \\Delta y_{t-1} + \\theta_1 \\epsilon_{t-1} + \\epsilon_{t}\n", "$$\n", "\n", "where $c$ is the intercept of the ARMA model, $\\Delta$ is the first-difference operator, and we assume $\\epsilon_{t} \\sim N(0, \\sigma^2)$. This can be rewritten to emphasize lag polynomials as (this will be useful in example 2, below):\n", "\n", "$$\n", "(1 - \\phi_1 L ) \\Delta y_t = c + (1 + \\theta_1 L) \\epsilon_{t}\n", "$$\n", "\n", "where $L$ is the lag operator.\n", "\n", "Notice that one difference between the Stata output and the output below is that Stata estimates the following model:\n", "\n", "$$\n", "(\\Delta y_t - \\beta_0) = \\phi_1 ( \\Delta y_{t-1} - \\beta_0) + \\theta_1 \\epsilon_{t-1} + \\epsilon_{t}\n", "$$\n", "\n", "where $\\beta_0$ is the mean of the process $y_t$. This model is equivalent to the one estimated in the statsmodels SARIMAX class, but the interpretation is different. To see the equivalence, note that:\n", "\n", "$$\n", "(\\Delta y_t - \\beta_0) = \\phi_1 ( \\Delta y_{t-1} - \\beta_0) + \\theta_1 \\epsilon_{t-1} + \\epsilon_{t} \\\\\n", "\\Delta y_t = (1 - \\phi_1) \\beta_0 + \\phi_1 \\Delta y_{t-1} + \\theta_1 \\epsilon_{t-1} + \\epsilon_{t}\n", "$$\n", "\n", "so that $c = (1 - \\phi_1) \\beta_0$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " SARIMAX Results \n", "==============================================================================\n", "Dep. Variable: wpi No. Observations: 124\n", "Model: SARIMAX(1, 1, 1) Log Likelihood -135.351\n", "Date: Fri, 21 Feb 2020 AIC 278.703\n", "Time: 13:56:15 BIC 289.951\n", "Sample: 01-01-1960 HQIC 283.272\n", " - 10-01-1990 \n", "Covariance Type: opg \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "intercept 0.0943 0.068 1.389 0.165 -0.039 0.227\n", "ar.L1 0.8742 0.055 16.028 0.000 0.767 0.981\n", "ma.L1 -0.4120 0.100 -4.119 0.000 -0.608 -0.216\n", "sigma2 0.5257 0.053 9.849 0.000 0.421 0.630\n", "===================================================================================\n", "Ljung-Box (Q): 37.12 Jarque-Bera (JB): 9.78\n", "Prob(Q): 0.60 Prob(JB): 0.01\n", "Heteroskedasticity (H): 15.93 Skew: 0.28\n", "Prob(H) (two-sided): 0.00 Kurtosis: 4.26\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n" ] } ], "source": [ "# Dataset\n", "wpi1 = requests.get('https://www.stata-press.com/data/r12/wpi1.dta').content\n", "data = pd.read_stata(BytesIO(wpi1))\n", "data.index = data.t\n", "# Set the frequency\n", "data.index.freq=\"QS-OCT\"\n", "\n", "# Fit the model\n", "mod = sm.tsa.statespace.SARIMAX(data['wpi'], trend='c', order=(1,1,1))\n", "res = mod.fit(disp=False)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Thus the maximum likelihood estimates imply that for the process above, we have:\n", "\n", "$$\n", "\\Delta y_t = 0.1050 + 0.8742 \\Delta y_{t-1} - 0.4120 \\epsilon_{t-1} + \\epsilon_{t}\n", "$$\n", "\n", "where $\\epsilon_{t} \\sim N(0, 0.5257)$. Finally, recall that $c = (1 - \\phi_1) \\beta_0$, and here $c = 0.0943$ and $\\phi_1 = 0.8742$. To compare with the output from Stata, we could calculate the mean:\n", "\n", "$$\\beta_0 = \\frac{c}{1 - \\phi_1} = \\frac{0.0943}{1 - 0.8742} = 0.7496$$\n", "\n", "**Note**: these values are slightly different from the values in the Stata documentation because the optimizer in statsmodels has found parameters here that yield a higher likelihood. Nonetheless, they are very close." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ARIMA Example 2: Arima with additive seasonal effects\n", "\n", "This model is an extension of that from example 1. Here the data is assumed to follow the process:\n", "\n", "$$\n", "\\Delta y_t = c + \\phi_1 \\Delta y_{t-1} + \\theta_1 \\epsilon_{t-1} + \\theta_4 \\epsilon_{t-4} + \\epsilon_{t}\n", "$$\n", "\n", "The new part of this model is that there is allowed to be a annual seasonal effect (it is annual even though the periodicity is 4 because the dataset is quarterly). The second difference is that this model uses the log of the data rather than the level.\n", "\n", "Before estimating the dataset, graphs showing:\n", "\n", "1. The time series (in logs)\n", "2. The first difference of the time series (in logs)\n", "3. The autocorrelation function\n", "4. The partial autocorrelation function.\n", "\n", "From the first two graphs, we note that the original time series does not appear to be stationary, whereas the first-difference does. This supports either estimating an ARMA model on the first-difference of the data, or estimating an ARIMA model with 1 order of integration (recall that we are taking the latter approach). The last two graphs support the use of an ARMA(1,1,1) model." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# Dataset\n", "data = pd.read_stata(BytesIO(wpi1))\n", "data.index = data.t\n", "data.index.freq=\"QS-OCT\"\n", "\n", "data['ln_wpi'] = np.log(data['wpi'])\n", "data['D.ln_wpi'] = data['ln_wpi'].diff()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Graph data\n", "fig, axes = plt.subplots(1, 2, figsize=(15,4))\n", "\n", "# Levels\n", "axes[0].plot(data.index._mpl_repr(), data['wpi'], '-')\n", "axes[0].set(title='US Wholesale Price Index')\n", "\n", "# Log difference\n", "axes[1].plot(data.index._mpl_repr(), data['D.ln_wpi'], '-')\n", "axes[1].hlines(0, data.index[0], data.index[-1], 'r')\n", "axes[1].set(title='US Wholesale Price Index - difference of logs');" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Graph data\n", "fig, axes = plt.subplots(1, 2, figsize=(15,4))\n", "\n", "fig = sm.graphics.tsa.plot_acf(data.iloc[1:]['D.ln_wpi'], lags=40, ax=axes[0])\n", "fig = sm.graphics.tsa.plot_pacf(data.iloc[1:]['D.ln_wpi'], lags=40, ax=axes[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To understand how to specify this model in statsmodels, first recall that from example 1 we used the following code to specify the ARIMA(1,1,1) model:\n", "\n", "```python\n", "mod = sm.tsa.statespace.SARIMAX(data['wpi'], trend='c', order=(1,1,1))\n", "```\n", "\n", "The `order` argument is a tuple of the form `(AR specification, Integration order, MA specification)`. The integration order must be an integer (for example, here we assumed one order of integration, so it was specified as 1. In a pure ARMA model where the underlying data is already stationary, it would be 0).\n", "\n", "For the AR specification and MA specification components, there are two possibilities. The first is to specify the **maximum degree** of the corresponding lag polynomial, in which case the component is an integer. For example, if we wanted to specify an ARIMA(1,1,4) process, we would use:\n", "\n", "```python\n", "mod = sm.tsa.statespace.SARIMAX(data['wpi'], trend='c', order=(1,1,4))\n", "```\n", "\n", "and the corresponding data process would be:\n", "\n", "$$\n", "y_t = c + \\phi_1 y_{t-1} + \\theta_1 \\epsilon_{t-1} + \\theta_2 \\epsilon_{t-2} + \\theta_3 \\epsilon_{t-3} + \\theta_4 \\epsilon_{t-4} + \\epsilon_{t}\n", "$$\n", "\n", "or\n", "\n", "$$\n", "(1 - \\phi_1 L)\\Delta y_t = c + (1 + \\theta_1 L + \\theta_2 L^2 + \\theta_3 L^3 + \\theta_4 L^4) \\epsilon_{t}\n", "$$\n", "\n", "When the specification parameter is given as a maximum degree of the lag polynomial, it implies that all polynomial terms up to that degree are included. Notice that this is *not* the model we want to use, because it would include terms for $\\epsilon_{t-2}$ and $\\epsilon_{t-3}$, which we do not want here.\n", "\n", "What we want is a polynomial that has terms for the 1st and 4th degrees, but leaves out the 2nd and 3rd terms. To do that, we need to provide a tuple for the specification parameter, where the tuple describes **the lag polynomial itself**. In particular, here we would want to use:\n", "\n", "```python\n", "ar = 1 # this is the maximum degree specification\n", "ma = (1,0,0,1) # this is the lag polynomial specification\n", "mod = sm.tsa.statespace.SARIMAX(data['wpi'], trend='c', order=(ar,1,ma)))\n", "```\n", "\n", "This gives the following form for the process of the data:\n", "\n", "$$\n", "\\Delta y_t = c + \\phi_1 \\Delta y_{t-1} + \\theta_1 \\epsilon_{t-1} + \\theta_4 \\epsilon_{t-4} + \\epsilon_{t} \\\\\n", "(1 - \\phi_1 L)\\Delta y_t = c + (1 + \\theta_1 L + \\theta_4 L^4) \\epsilon_{t}\n", "$$\n", "\n", "which is what we want." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " SARIMAX Results \n", "=================================================================================\n", "Dep. Variable: ln_wpi No. Observations: 124\n", "Model: SARIMAX(1, 1, [1, 4]) Log Likelihood 386.033\n", "Date: Fri, 21 Feb 2020 AIC -762.067\n", "Time: 13:56:16 BIC -748.006\n", "Sample: 01-01-1960 HQIC -756.355\n", " - 10-01-1990 \n", "Covariance Type: opg \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "intercept 0.0024 0.002 1.489 0.137 -0.001 0.006\n", "ar.L1 0.7800 0.094 8.254 0.000 0.595 0.965\n", "ma.L1 -0.3981 0.126 -3.165 0.002 -0.645 -0.152\n", "ma.L4 0.3096 0.120 2.581 0.010 0.074 0.545\n", "sigma2 0.0001 9.8e-06 11.110 0.000 8.97e-05 0.000\n", "===================================================================================\n", "Ljung-Box (Q): 30.07 Jarque-Bera (JB): 45.15\n", "Prob(Q): 0.87 Prob(JB): 0.00\n", "Heteroskedasticity (H): 2.57 Skew: 0.29\n", "Prob(H) (two-sided): 0.00 Kurtosis: 5.91\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n" ] } ], "source": [ "# Fit the model\n", "mod = sm.tsa.statespace.SARIMAX(data['ln_wpi'], trend='c', order=(1,1,(1,0,0,1)))\n", "res = mod.fit(disp=False)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ARIMA Example 3: Airline Model\n", "\n", "In the previous example, we included a seasonal effect in an *additive* way, meaning that we added a term allowing the process to depend on the 4th MA lag. It may be instead that we want to model a seasonal effect in a multiplicative way. We often write the model then as an ARIMA $(p,d,q) \\times (P,D,Q)_s$, where the lowercase letters indicate the specification for the non-seasonal component, and the uppercase letters indicate the specification for the seasonal component; $s$ is the periodicity of the seasons (e.g. it is often 4 for quarterly data or 12 for monthly data). The data process can be written generically as:\n", "\n", "$$\n", "\\phi_p (L) \\tilde \\phi_P (L^s) \\Delta^d \\Delta_s^D y_t = A(t) + \\theta_q (L) \\tilde \\theta_Q (L^s) \\epsilon_t\n", "$$\n", "\n", "where:\n", "\n", "- $\\phi_p (L)$ is the non-seasonal autoregressive lag polynomial\n", "- $\\tilde \\phi_P (L^s)$ is the seasonal autoregressive lag polynomial\n", "- $\\Delta^d \\Delta_s^D y_t$ is the time series, differenced $d$ times, and seasonally differenced $D$ times.\n", "- $A(t)$ is the trend polynomial (including the intercept)\n", "- $\\theta_q (L)$ is the non-seasonal moving average lag polynomial\n", "- $\\tilde \\theta_Q (L^s)$ is the seasonal moving average lag polynomial\n", "\n", "sometimes we rewrite this as:\n", "\n", "$$\n", "\\phi_p (L) \\tilde \\phi_P (L^s) y_t^* = A(t) + \\theta_q (L) \\tilde \\theta_Q (L^s) \\epsilon_t\n", "$$\n", "\n", "where $y_t^* = \\Delta^d \\Delta_s^D y_t$. This emphasizes that just as in the simple case, after we take differences (here both non-seasonal and seasonal) to make the data stationary, the resulting model is just an ARMA model.\n", "\n", "As an example, consider the airline model ARIMA $(2,1,0) \\times (1,1,0)_{12}$, with an intercept. The data process can be written in the form above as:\n", "\n", "$$\n", "(1 - \\phi_1 L - \\phi_2 L^2) (1 - \\tilde \\phi_1 L^{12}) \\Delta \\Delta_{12} y_t = c + \\epsilon_t\n", "$$\n", "\n", "Here, we have:\n", "\n", "- $\\phi_p (L) = (1 - \\phi_1 L - \\phi_2 L^2)$\n", "- $\\tilde \\phi_P (L^s) = (1 - \\phi_1 L^12)$\n", "- $d = 1, D = 1, s=12$ indicating that $y_t^*$ is derived from $y_t$ by taking first-differences and then taking 12-th differences.\n", "- $A(t) = c$ is the *constant* trend polynomial (i.e. just an intercept)\n", "- $\\theta_q (L) = \\tilde \\theta_Q (L^s) = 1$ (i.e. there is no moving average effect)\n", "\n", "It may still be confusing to see the two lag polynomials in front of the time-series variable, but notice that we can multiply the lag polynomials together to get the following model:\n", "\n", "$$\n", "(1 - \\phi_1 L - \\phi_2 L^2 - \\tilde \\phi_1 L^{12} + \\phi_1 \\tilde \\phi_1 L^{13} + \\phi_2 \\tilde \\phi_1 L^{14} ) y_t^* = c + \\epsilon_t\n", "$$\n", "\n", "which can be rewritten as:\n", "\n", "$$\n", "y_t^* = c + \\phi_1 y_{t-1}^* + \\phi_2 y_{t-2}^* + \\tilde \\phi_1 y_{t-12}^* - \\phi_1 \\tilde \\phi_1 y_{t-13}^* - \\phi_2 \\tilde \\phi_1 y_{t-14}^* + \\epsilon_t\n", "$$\n", "\n", "This is similar to the additively seasonal model from example 2, but the coefficients in front of the autoregressive lags are actually combinations of the underlying seasonal and non-seasonal parameters.\n", "\n", "Specifying the model in statsmodels is done simply by adding the `seasonal_order` argument, which accepts a tuple of the form `(Seasonal AR specification, Seasonal Integration order, Seasonal MA, Seasonal periodicity)`. The seasonal AR and MA specifications, as before, can be expressed as a maximum polynomial degree or as the lag polynomial itself. Seasonal periodicity is an integer.\n", "\n", "For the airline model ARIMA $(2,1,0) \\times (1,1,0)_{12}$ with an intercept, the command is:\n", "\n", "```python\n", "mod = sm.tsa.statespace.SARIMAX(data['lnair'], order=(2,1,0), seasonal_order=(1,1,0,12))\n", "```" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " SARIMAX Results \n", "==========================================================================================\n", "Dep. Variable: D.DS12.lnair No. Observations: 131\n", "Model: SARIMAX(2, 0, 0)x(1, 0, 0, 12) Log Likelihood 240.821\n", "Date: Fri, 21 Feb 2020 AIC -473.643\n", "Time: 13:56:16 BIC -462.142\n", "Sample: 02-01-1950 HQIC -468.970\n", " - 12-01-1960 \n", "Covariance Type: opg \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "ar.L1 -0.4057 0.080 -5.045 0.000 -0.563 -0.248\n", "ar.L2 -0.0799 0.099 -0.809 0.419 -0.274 0.114\n", "ar.S.L12 -0.4723 0.072 -6.592 0.000 -0.613 -0.332\n", "sigma2 0.0014 0.000 8.403 0.000 0.001 0.002\n", "===================================================================================\n", "Ljung-Box (Q): 49.89 Jarque-Bera (JB): 0.72\n", "Prob(Q): 0.14 Prob(JB): 0.70\n", "Heteroskedasticity (H): 0.54 Skew: 0.14\n", "Prob(H) (two-sided): 0.04 Kurtosis: 3.23\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n" ] } ], "source": [ "# Dataset\n", "air2 = requests.get('https://www.stata-press.com/data/r12/air2.dta').content\n", "data = pd.read_stata(BytesIO(air2))\n", "data.index = pd.date_range(start=datetime(data.time[0], 1, 1), periods=len(data), freq='MS')\n", "data['lnair'] = np.log(data['air'])\n", "\n", "# Fit the model\n", "mod = sm.tsa.statespace.SARIMAX(data['lnair'], order=(2,1,0), seasonal_order=(1,1,0,12), simple_differencing=True)\n", "res = mod.fit(disp=False)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice that here we used an additional argument `simple_differencing=True`. This controls how the order of integration is handled in ARIMA models. If `simple_differencing=True`, then the time series provided as `endog` is literally differenced and an ARMA model is fit to the resulting new time series. This implies that a number of initial periods are lost to the differencing process, however it may be necessary either to compare results to other packages (e.g. Stata's `arima` always uses simple differencing) or if the seasonal periodicity is large.\n", "\n", "The default is `simple_differencing=False`, in which case the integration component is implemented as part of the state space formulation, and all of the original data can be used in estimation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ARIMA Example 4: ARMAX (Friedman)\n", "\n", "This model demonstrates the use of explanatory variables (the X part of ARMAX). When exogenous regressors are included, the SARIMAX module uses the concept of \"regression with SARIMA errors\" (see http://robjhyndman.com/hyndsight/arimax/ for details of regression with ARIMA errors versus alternative specifications), so that the model is specified as:\n", "\n", "$$\n", "y_t = \\beta_t x_t + u_t \\\\\n", " \\phi_p (L) \\tilde \\phi_P (L^s) \\Delta^d \\Delta_s^D u_t = A(t) +\n", " \\theta_q (L) \\tilde \\theta_Q (L^s) \\epsilon_t\n", "$$\n", "\n", "Notice that the first equation is just a linear regression, and the second equation just describes the process followed by the error component as SARIMA (as was described in example 3). One reason for this specification is that the estimated parameters have their natural interpretations.\n", "\n", "This specification nests many simpler specifications. For example, regression with AR(2) errors is:\n", "\n", "$$\n", "y_t = \\beta_t x_t + u_t \\\\\n", "(1 - \\phi_1 L - \\phi_2 L^2) u_t = A(t) + \\epsilon_t\n", "$$\n", "\n", "The model considered in this example is regression with ARMA(1,1) errors. The process is then written:\n", "\n", "$$\n", "\\text{consump}_t = \\beta_0 + \\beta_1 \\text{m2}_t + u_t \\\\\n", "(1 - \\phi_1 L) u_t = (1 - \\theta_1 L) \\epsilon_t\n", "$$\n", "\n", "Notice that $\\beta_0$ is, as described in example 1 above, *not* the same thing as an intercept specified by `trend='c'`. Whereas in the examples above we estimated the intercept of the model via the trend polynomial, here, we demonstrate how to estimate $\\beta_0$ itself by adding a constant to the exogenous dataset. In the output, the $beta_0$ is called `const`, whereas above the intercept $c$ was called `intercept` in the output." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " SARIMAX Results \n", "==============================================================================\n", "Dep. Variable: consump No. Observations: 92\n", "Model: SARIMAX(1, 0, 1) Log Likelihood -340.508\n", "Date: Fri, 21 Feb 2020 AIC 691.015\n", "Time: 13:56:17 BIC 703.624\n", "Sample: 01-01-1959 HQIC 696.105\n", " - 10-01-1981 \n", "Covariance Type: opg \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const -36.0618 56.647 -0.637 0.524 -147.088 74.964\n", "m2 1.1220 0.036 30.823 0.000 1.051 1.193\n", "ar.L1 0.9349 0.041 22.717 0.000 0.854 1.016\n", "ma.L1 0.3091 0.089 3.488 0.000 0.135 0.483\n", "sigma2 93.2547 10.888 8.565 0.000 71.914 114.596\n", "===================================================================================\n", "Ljung-Box (Q): 38.72 Jarque-Bera (JB): 23.50\n", "Prob(Q): 0.53 Prob(JB): 0.00\n", "Heteroskedasticity (H): 22.51 Skew: 0.17\n", "Prob(H) (two-sided): 0.00 Kurtosis: 5.45\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n" ] } ], "source": [ "# Dataset\n", "friedman2 = requests.get('https://www.stata-press.com/data/r12/friedman2.dta').content\n", "data = pd.read_stata(BytesIO(friedman2))\n", "data.index = data.time\n", "data.index.freq = \"QS-OCT\"\n", "\n", "# Variables\n", "endog = data.loc['1959':'1981', 'consump']\n", "exog = sm.add_constant(data.loc['1959':'1981', 'm2'])\n", "\n", "# Fit the model\n", "mod = sm.tsa.statespace.SARIMAX(endog, exog, order=(1,0,1))\n", "res = mod.fit(disp=False)\n", "print(res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ARIMA Postestimation: Example 1 - Dynamic Forecasting\n", "\n", "Here we describe some of the post-estimation capabilities of statsmodels' SARIMAX.\n", "\n", "First, using the model from example, we estimate the parameters using data that *excludes the last few observations* (this is a little artificial as an example, but it allows considering performance of out-of-sample forecasting and facilitates comparison to Stata's documentation)." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " SARIMAX Results \n", "==============================================================================\n", "Dep. Variable: consump No. Observations: 77\n", "Model: SARIMAX(1, 0, 1) Log Likelihood -243.316\n", "Date: Fri, 21 Feb 2020 AIC 496.633\n", "Time: 13:56:17 BIC 508.352\n", "Sample: 01-01-1959 HQIC 501.320\n", " - 01-01-1978 \n", "Covariance Type: opg \n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const 0.6771 18.490 0.037 0.971 -35.563 36.917\n", "m2 1.0379 0.021 50.332 0.000 0.997 1.078\n", "ar.L1 0.8775 0.059 14.860 0.000 0.762 0.993\n", "ma.L1 0.2771 0.108 2.572 0.010 0.066 0.488\n", "sigma2 31.6970 4.683 6.769 0.000 22.519 40.875\n", "===================================================================================\n", "Ljung-Box (Q): 46.78 Jarque-Bera (JB): 6.05\n", "Prob(Q): 0.21 Prob(JB): 0.05\n", "Heteroskedasticity (H): 6.09 Skew: 0.57\n", "Prob(H) (two-sided): 0.00 Kurtosis: 3.76\n", "===================================================================================\n", "\n", "Warnings:\n", "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n" ] } ], "source": [ "# Dataset\n", "raw = pd.read_stata(BytesIO(friedman2))\n", "raw.index = raw.time\n", "raw.index.freq = \"QS-OCT\"\n", "data = raw.loc[:'1981']\n", "\n", "# Variables\n", "endog = data.loc['1959':, 'consump']\n", "exog = sm.add_constant(data.loc['1959':, 'm2'])\n", "nobs = endog.shape[0]\n", "\n", "# Fit the model\n", "mod = sm.tsa.statespace.SARIMAX(endog.loc[:'1978-01-01'], exog=exog.loc[:'1978-01-01'], order=(1,0,1))\n", "fit_res = mod.fit(disp=False)\n", "print(fit_res.summary())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we want to get results for the full dataset but using the estimated parameters (on a subset of the data)." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "mod = sm.tsa.statespace.SARIMAX(endog, exog=exog, order=(1,0,1))\n", "res = mod.filter(fit_res.params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `predict` command is first applied here to get in-sample predictions. We use the `full_results=True` argument to allow us to calculate confidence intervals (the default output of `predict` is just the predicted values).\n", "\n", "With no other arguments, `predict` returns the one-step-ahead in-sample predictions for the entire sample." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# In-sample one-step-ahead predictions\n", "predict = res.get_prediction()\n", "predict_ci = predict.conf_int()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also get *dynamic predictions*. One-step-ahead prediction uses the true values of the endogenous values at each step to predict the next in-sample value. Dynamic predictions use one-step-ahead prediction up to some point in the dataset (specified by the `dynamic` argument); after that, the previous *predicted* endogenous values are used in place of the true endogenous values for each new predicted element.\n", "\n", "The `dynamic` argument is specified to be an *offset* relative to the `start` argument. If `start` is not specified, it is assumed to be `0`.\n", "\n", "Here we perform dynamic prediction starting in the first quarter of 1978." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# Dynamic predictions\n", "predict_dy = res.get_prediction(dynamic='1978-01-01')\n", "predict_dy_ci = predict_dy.conf_int()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can graph the one-step-ahead and dynamic predictions (and the corresponding confidence intervals) to see their relative performance. Notice that up to the point where dynamic prediction begins (1978:Q1), the two are the same." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Graph\n", "fig, ax = plt.subplots(figsize=(9,4))\n", "npre = 4\n", "ax.set(title='Personal consumption', xlabel='Date', ylabel='Billions of dollars')\n", "\n", "# Plot data points\n", "data.loc['1977-07-01':, 'consump'].plot(ax=ax, style='o', label='Observed')\n", "\n", "# Plot predictions\n", "predict.predicted_mean.loc['1977-07-01':].plot(ax=ax, style='r--', label='One-step-ahead forecast')\n", "ci = predict_ci.loc['1977-07-01':]\n", "ax.fill_between(ci.index, ci.iloc[:,0], ci.iloc[:,1], color='r', alpha=0.1)\n", "predict_dy.predicted_mean.loc['1977-07-01':].plot(ax=ax, style='g', label='Dynamic forecast (1978)')\n", "ci = predict_dy_ci.loc['1977-07-01':]\n", "ax.fill_between(ci.index, ci.iloc[:,0], ci.iloc[:,1], color='g', alpha=0.1)\n", "\n", "legend = ax.legend(loc='lower right')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, graph the prediction *error*. It is obvious that, as one would suspect, one-step-ahead prediction is considerably better." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Prediction error\n", "\n", "# Graph\n", "fig, ax = plt.subplots(figsize=(9,4))\n", "npre = 4\n", "ax.set(title='Forecast error', xlabel='Date', ylabel='Forecast - Actual')\n", "\n", "# In-sample one-step-ahead predictions and 95% confidence intervals\n", "predict_error = predict.predicted_mean - endog\n", "predict_error.loc['1977-10-01':].plot(ax=ax, label='One-step-ahead forecast')\n", "ci = predict_ci.loc['1977-10-01':].copy()\n", "ci.iloc[:,0] -= endog.loc['1977-10-01':]\n", "ci.iloc[:,1] -= endog.loc['1977-10-01':]\n", "ax.fill_between(ci.index, ci.iloc[:,0], ci.iloc[:,1], alpha=0.1)\n", "\n", "# Dynamic predictions and 95% confidence intervals\n", "predict_dy_error = predict_dy.predicted_mean - endog\n", "predict_dy_error.loc['1977-10-01':].plot(ax=ax, style='r', label='Dynamic forecast (1978)')\n", "ci = predict_dy_ci.loc['1977-10-01':].copy()\n", "ci.iloc[:,0] -= endog.loc['1977-10-01':]\n", "ci.iloc[:,1] -= endog.loc['1977-10-01':]\n", "ax.fill_between(ci.index, ci.iloc[:,0], ci.iloc[:,1], color='r', alpha=0.1)\n", "\n", "legend = ax.legend(loc='lower left');\n", "legend.get_frame().set_facecolor('w')" ] } ], "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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 1 }