{ "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: Tue, 17 Dec 2019 AIC 278.703\n", "Time: 23:39:53 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 386.034\n", "Date: Tue, 17 Dec 2019 AIC -762.067\n", "Time: 23:39:54 BIC -748.006\n", "Sample: 01-01-1960 HQIC -756.356\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 1.486 0.137 -0.001 0.006\n", "ar.L1 0.7804 0.094 8.259 0.000 0.595 0.966\n", "ma.L1 -0.3992 0.126 -3.175 0.001 -0.646 -0.153\n", "ma.L4 0.3097 0.120 2.581 0.010 0.075 0.545\n", "sigma2 0.0001 9.81e-06 11.107 0.000 8.97e-05 0.000\n", "===================================================================================\n", "Ljung-Box (Q): 30.04 Jarque-Bera (JB): 45.05\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: Tue, 17 Dec 2019 AIC -473.643\n", "Time: 23:39:55 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": "stderr", "output_type": "stream", "text": [ "/home/travis/miniconda/envs/statsmodels-test/lib/python3.7/site-packages/numpy/core/fromnumeric.py:2495: FutureWarning: Method .ptp is deprecated and will be removed in a future version. Use numpy.ptp instead.\n", " return ptp(axis=axis, out=out, **kwargs)\n" ] }, { "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: Tue, 17 Dec 2019 AIC 691.015\n", "Time: 23:39:56 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 -36.0608 56.645 -0.637 0.524 -147.084 74.962\n", "m2 1.1220 0.036 30.824 0.000 1.051 1.193\n", "ar.L1 0.9348 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 93.2548 10.888 8.565 0.000 71.914 114.596\n", "===================================================================================\n", "Ljung-Box (Q): 38.72 Jarque-Bera (JB): 23.49\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: Tue, 17 Dec 2019 AIC 496.633\n", "Time: 23:39:56 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 0.6782 18.492 0.037 0.971 -35.565 36.921\n", "m2 1.0379 0.021 50.329 0.000 0.997 1.078\n", "ar.L1 0.8775 0.059 14.859 0.000 0.762 0.993\n", "ma.L1 0.2771 0.108 2.572 0.010 0.066 0.488\n", "sigma2 31.6979 4.683 6.769 0.000 22.520 40.876\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": "3.7.5" } }, "nbformat": 4, "nbformat_minor": 1 }