{
 "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:26.301153Z",
     "iopub.status.busy": "2021-02-02T06:55:26.300080Z",
     "iopub.status.idle": "2021-02-02T06:55:26.529087Z",
     "shell.execute_reply": "2021-02-02T06:55:26.528597Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:26.534845Z",
     "iopub.status.busy": "2021-02-02T06:55:26.533084Z",
     "iopub.status.idle": "2021-02-02T06:55:27.182510Z",
     "shell.execute_reply": "2021-02-02T06:55:27.182876Z"
    }
   },
   "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()\n",
    "plt.rc(\"figure\", figsize=(16,8))\n",
    "plt.rc(\"font\", size=14)"
   ]
  },
  {
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:27.190265Z",
     "iopub.status.busy": "2021-02-02T06:55:27.187509Z",
     "iopub.status.idle": "2021-02-02T06:55:27.505506Z",
     "shell.execute_reply": "2021-02-02T06:55:27.506561Z"
    }
   },
   "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, 02 Feb 2021   AIC                            278.703\n",
      "Time:                        06:55:27   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 (L1) (Q):                   0.09   Jarque-Bera (JB):                 9.78\n",
      "Prob(Q):                              0.77   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",
    "$$\n",
    "\\Delta y_t = 0.0943 + 0.8742 \\Delta y_{t-1} - 0.4120 \\epsilon_{t-1} + \\epsilon_{t}\n",
    "$$\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**: This value is virtually identical to the value in the Stata documentation, $\\beta_0 = 0.7498$. The slight difference is likely down to rounding and subtle differences in stopping criterion of the numerical optimizers used."
   ]
  },
  {
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:27.511236Z",
     "iopub.status.busy": "2021-02-02T06:55:27.509882Z",
     "iopub.status.idle": "2021-02-02T06:55:27.531045Z",
     "shell.execute_reply": "2021-02-02T06:55:27.532053Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:27.540638Z",
     "iopub.status.busy": "2021-02-02T06:55:27.535127Z",
     "iopub.status.idle": "2021-02-02T06:55:28.027453Z",
     "shell.execute_reply": "2021-02-02T06:55:28.028575Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0.5, 1.0, 'US Wholesale Price Index - difference of logs')]"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 2 Axes>"
      ]
     },
     "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:28.033695Z",
     "iopub.status.busy": "2021-02-02T06:55:28.032232Z",
     "iopub.status.idle": "2021-02-02T06:55:28.453844Z",
     "shell.execute_reply": "2021-02-02T06:55:28.454936Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x288 with 2 Axes>"
      ]
     },
     "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:28.459841Z",
     "iopub.status.busy": "2021-02-02T06:55:28.458410Z",
     "iopub.status.idle": "2021-02-02T06:55:28.983479Z",
     "shell.execute_reply": "2021-02-02T06:55:28.984661Z"
    }
   },
   "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, 02 Feb 2021   AIC                           -762.067\n",
      "Time:                           06:55:28   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      1.489      0.136      -0.001       0.006\n",
      "ar.L1          0.7801      0.095      8.247      0.000       0.595       0.965\n",
      "ma.L1         -0.3986      0.126     -3.165      0.002      -0.645      -0.152\n",
      "ma.L4          0.3092      0.120      2.575      0.010       0.074       0.545\n",
      "sigma2         0.0001   9.81e-06     11.108      0.000    8.97e-05       0.000\n",
      "===================================================================================\n",
      "Ljung-Box (L1) (Q):                   0.02   Jarque-Bera (JB):                45.14\n",
      "Prob(Q):                              0.90   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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:28.990050Z",
     "iopub.status.busy": "2021-02-02T06:55:28.988385Z",
     "iopub.status.idle": "2021-02-02T06:55:29.491243Z",
     "shell.execute_reply": "2021-02-02T06:55:29.492456Z"
    }
   },
   "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, 02 Feb 2021   AIC                           -473.643\n",
      "Time:                                    06:55:29   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 (L1) (Q):                   0.01   Jarque-Bera (JB):                 0.72\n",
      "Prob(Q):                              0.91   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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:29.498164Z",
     "iopub.status.busy": "2021-02-02T06:55:29.496516Z",
     "iopub.status.idle": "2021-02-02T06:55:30.045360Z",
     "shell.execute_reply": "2021-02-02T06:55:30.046581Z"
    }
   },
   "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:                Tue, 02 Feb 2021   AIC                            691.015\n",
      "Time:                        06:55:30   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        -36.0606     56.643     -0.637      0.524    -147.078      74.957\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       1.015\n",
      "ma.L1          0.3091      0.089      3.488      0.000       0.135       0.483\n",
      "sigma2        93.2556     10.889      8.565      0.000      71.914     114.597\n",
      "===================================================================================\n",
      "Ljung-Box (L1) (Q):                   0.04   Jarque-Bera (JB):                23.49\n",
      "Prob(Q):                              0.84   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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:30.052114Z",
     "iopub.status.busy": "2021-02-02T06:55:30.050415Z",
     "iopub.status.idle": "2021-02-02T06:55:30.519401Z",
     "shell.execute_reply": "2021-02-02T06:55:30.520575Z"
    }
   },
   "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, 02 Feb 2021   AIC                            496.633\n",
      "Time:                        06:55:30   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          0.6765     18.490      0.037      0.971     -35.563      36.916\n",
      "m2             1.0379      0.021     50.333      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        31.6977      4.683      6.769      0.000      22.519      40.876\n",
      "===================================================================================\n",
      "Ljung-Box (L1) (Q):                   0.32   Jarque-Bera (JB):                 6.05\n",
      "Prob(Q):                              0.57   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"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/travis/build/statsmodels/statsmodels/statsmodels/base/model.py:568: ConvergenceWarning: Maximum Likelihood optimization failed to converge. Check mle_retvals\n",
      "  ConvergenceWarning)\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, maxiter=250)\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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:30.526028Z",
     "iopub.status.busy": "2021-02-02T06:55:30.524431Z",
     "iopub.status.idle": "2021-02-02T06:55:30.552619Z",
     "shell.execute_reply": "2021-02-02T06:55:30.553767Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:30.559031Z",
     "iopub.status.busy": "2021-02-02T06:55:30.557431Z",
     "iopub.status.idle": "2021-02-02T06:55:30.565781Z",
     "shell.execute_reply": "2021-02-02T06:55:30.566955Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:30.572103Z",
     "iopub.status.busy": "2021-02-02T06:55:30.570519Z",
     "iopub.status.idle": "2021-02-02T06:55:30.582517Z",
     "shell.execute_reply": "2021-02-02T06:55:30.583652Z"
    }
   },
   "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:30.588685Z",
     "iopub.status.busy": "2021-02-02T06:55:30.587072Z",
     "iopub.status.idle": "2021-02-02T06:55:30.966061Z",
     "shell.execute_reply": "2021-02-02T06:55:30.967241Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x288 with 1 Axes>"
      ]
     },
     "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": {
    "execution": {
     "iopub.execute_input": "2021-02-02T06:55:30.972677Z",
     "iopub.status.busy": "2021-02-02T06:55:30.971045Z",
     "iopub.status.idle": "2021-02-02T06:55:31.335617Z",
     "shell.execute_reply": "2021-02-02T06:55:31.336809Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x288 with 1 Axes>"
      ]
     },
     "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": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}