{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Forecasting in statsmodels\n",
    "\n",
    "This notebook describes forecasting using time series models in statsmodels.\n",
    "\n",
    "**Note**: this notebook applies only to the state space model classes, which are:\n",
    "\n",
    "- `sm.tsa.SARIMAX`\n",
    "- `sm.tsa.UnobservedComponents`\n",
    "- `sm.tsa.VARMAX`\n",
    "- `sm.tsa.DynamicFactor`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:45.193054Z",
     "iopub.status.busy": "2026-07-16T14:25:45.192830Z",
     "iopub.status.idle": "2026-07-16T14:25:50.766691Z",
     "shell.execute_reply": "2026-07-16T14:25:50.764262Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "\n",
    "macrodata = sm.datasets.macrodata.load_pandas().data\n",
    "macrodata.index = pd.period_range(\"1959Q1\", \"2009Q3\", freq=\"Q\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic example\n",
    "\n",
    "A simple example is to use an AR(1) model to forecast inflation. Before forecasting, let's take a look at the series:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:50.772303Z",
     "iopub.status.busy": "2026-07-16T14:25:50.771954Z",
     "iopub.status.idle": "2026-07-16T14:25:51.222512Z",
     "shell.execute_reply": "2026-07-16T14:25:51.220285Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: >"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "endog = macrodata[\"infl\"]\n",
    "endog.plot(figsize=(15, 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constructing and estimating the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next step is to formulate the econometric model that we want to use for forecasting. In this case, we will use an AR(1) model via the `SARIMAX` class in statsmodels.\n",
    "\n",
    "After constructing the model, we need to estimate its parameters. This is done using the `fit` method. The `summary` method produces several convenient tables showing the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:51.225505Z",
     "iopub.status.busy": "2026-07-16T14:25:51.225265Z",
     "iopub.status.idle": "2026-07-16T14:25:51.405837Z",
     "shell.execute_reply": "2026-07-16T14:25:51.402256Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                               SARIMAX Results                                \n",
      "==============================================================================\n",
      "Dep. Variable:                   infl   No. Observations:                  203\n",
      "Model:               SARIMAX(1, 0, 0)   Log Likelihood                -472.714\n",
      "Date:                Thu, 16 Jul 2026   AIC                            951.427\n",
      "Time:                        14:25:51   BIC                            961.367\n",
      "Sample:                    03-31-1959   HQIC                           955.449\n",
      "                         - 09-30-2009                                         \n",
      "Covariance Type:                  opg                                         \n",
      "==============================================================================\n",
      "                 coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "intercept      1.3962      0.254      5.488      0.000       0.898       1.895\n",
      "ar.L1          0.6441      0.039     16.482      0.000       0.568       0.721\n",
      "sigma2         6.1519      0.397     15.487      0.000       5.373       6.930\n",
      "===================================================================================\n",
      "Ljung-Box (L1) (Q):                   8.43   Jarque-Bera (JB):                68.45\n",
      "Prob(Q):                              0.00   Prob(JB):                         0.00\n",
      "Heteroskedasticity (H):               1.47   Skew:                            -0.22\n",
      "Prob(H) (two-sided):                  0.12   Kurtosis:                         5.81\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n"
     ]
    }
   ],
   "source": [
    "# Construct the model\n",
    "mod = sm.tsa.SARIMAX(endog, order=(1, 0, 0), trend=\"c\")\n",
    "# Estimate the parameters\n",
    "res = mod.fit()\n",
    "\n",
    "print(res.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Forecasting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Out-of-sample forecasts are produced using the `forecast` or `get_forecast` methods from the results object.\n",
    "\n",
    "The `forecast` method gives only point forecasts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:51.410924Z",
     "iopub.status.busy": "2026-07-16T14:25:51.410645Z",
     "iopub.status.idle": "2026-07-16T14:25:51.441690Z",
     "shell.execute_reply": "2026-07-16T14:25:51.439134Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2009Q4    3.68921\n",
      "Freq: Q-DEC, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# The default is to get a one-step-ahead forecast:\n",
    "print(res.forecast())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `get_forecast` method is more general, and also allows constructing confidence intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:51.446183Z",
     "iopub.status.busy": "2026-07-16T14:25:51.445923Z",
     "iopub.status.idle": "2026-07-16T14:25:51.483877Z",
     "shell.execute_reply": "2026-07-16T14:25:51.483156Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "infl       mean   mean_se  mean_ci_lower  mean_ci_upper\n",
      "2009Q4  3.68921  2.480302      -0.390523       7.768943\n"
     ]
    }
   ],
   "source": [
    "# Here we construct a more complete results object.\n",
    "fcast_res1 = res.get_forecast()\n",
    "\n",
    "# Most results are collected in the `summary_frame` attribute.\n",
    "# Here we specify that we want a confidence level of 90%\n",
    "print(fcast_res1.summary_frame(alpha=0.10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The default confidence level is 95%, but this can be controlled by setting the `alpha` parameter, where the confidence level is defined as $(1 - \\alpha) \\times 100\\%$. In the example above, we specified a confidence level of 90%, using `alpha=0.10`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Specifying the number of forecasts\n",
    "\n",
    "Both of the functions `forecast` and `get_forecast` accept a single argument indicating how many forecasting steps are desired. One option for this argument is always to provide an integer describing the number of steps ahead you want."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:51.489893Z",
     "iopub.status.busy": "2026-07-16T14:25:51.489621Z",
     "iopub.status.idle": "2026-07-16T14:25:51.516867Z",
     "shell.execute_reply": "2026-07-16T14:25:51.516104Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2009Q4    3.689210\n",
      "2010Q1    3.772434\n",
      "Freq: Q-DEC, Name: predicted_mean, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(res.forecast(steps=2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:51.522906Z",
     "iopub.status.busy": "2026-07-16T14:25:51.522626Z",
     "iopub.status.idle": "2026-07-16T14:25:51.544320Z",
     "shell.execute_reply": "2026-07-16T14:25:51.543598Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "infl        mean   mean_se  mean_ci_lower  mean_ci_upper\n",
      "2009Q4  3.689210  2.480302      -1.172092       8.550512\n",
      "2010Q1  3.772434  2.950274      -2.009996       9.554865\n"
     ]
    }
   ],
   "source": [
    "fcast_res2 = res.get_forecast(steps=2)\n",
    "# Note: since we did not specify the alpha parameter, the\n",
    "# confidence level is at the default, 95%\n",
    "print(fcast_res2.summary_frame())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, **if your data included a Pandas index with a defined frequency** (see the section at the end on Indexes for more information), then you can alternatively specify the date through which you want forecasts to be produced:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:51.549596Z",
     "iopub.status.busy": "2026-07-16T14:25:51.549319Z",
     "iopub.status.idle": "2026-07-16T14:25:51.570556Z",
     "shell.execute_reply": "2026-07-16T14:25:51.567585Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2009Q4    3.689210\n",
      "2010Q1    3.772434\n",
      "2010Q2    3.826039\n",
      "Freq: Q-DEC, Name: predicted_mean, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(res.forecast(\"2010Q2\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:51.580450Z",
     "iopub.status.busy": "2026-07-16T14:25:51.580119Z",
     "iopub.status.idle": "2026-07-16T14:25:51.616167Z",
     "shell.execute_reply": "2026-07-16T14:25:51.612855Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "infl        mean   mean_se  mean_ci_lower  mean_ci_upper\n",
      "2009Q4  3.689210  2.480302      -1.172092       8.550512\n",
      "2010Q1  3.772434  2.950274      -2.009996       9.554865\n",
      "2010Q2  3.826039  3.124571      -2.298008       9.950087\n"
     ]
    }
   ],
   "source": [
    "fcast_res3 = res.get_forecast(\"2010Q2\")\n",
    "print(fcast_res3.summary_frame())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the data, forecasts, and confidence intervals\n",
    "\n",
    "Often it is useful to plot the data, the forecasts, and the confidence intervals. There are many ways to do this, but here's one example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:51.620358Z",
     "iopub.status.busy": "2026-07-16T14:25:51.620094Z",
     "iopub.status.idle": "2026-07-16T14:25:52.170443Z",
     "shell.execute_reply": "2026-07-16T14:25:52.169386Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(15, 5))\n",
    "\n",
    "# Plot the data (here we are subsetting it to get a better look at the forecasts)\n",
    "endog.loc[\"1999\":].plot(ax=ax)\n",
    "\n",
    "# Construct the forecasts\n",
    "fcast = res.get_forecast(\"2011Q4\").summary_frame()\n",
    "fcast[\"mean\"].plot(ax=ax, style=\"k--\")\n",
    "ax.fill_between(\n",
    "    fcast.index, fcast[\"mean_ci_lower\"], fcast[\"mean_ci_upper\"], color=\"k\", alpha=0.1\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note on what to expect from forecasts\n",
    "\n",
    "The forecast above may not look very impressive, as it is almost a straight line. This is because this is a very simple, univariate forecasting model. Nonetheless, keep in mind that these simple forecasting models can be extremely competitive."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prediction vs Forecasting\n",
    "\n",
    "The results objects also contain two methods that all for both in-sample fitted values and out-of-sample forecasting. They are `predict` and `get_prediction`. The `predict` method only returns point predictions (similar to `forecast`), while the `get_prediction` method also returns additional results (similar to `get_forecast`).\n",
    "\n",
    "In general, if your interest is out-of-sample forecasting, it is easier to stick to the `forecast` and `get_forecast` methods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cross validation\n",
    "\n",
    "**Note**: some of the functions used in this section were first introduced in statsmodels v0.11.0.\n",
    "\n",
    "A common use case is to cross-validate forecasting methods by performing h-step-ahead forecasts recursively using the following process:\n",
    "\n",
    "1. Fit model parameters on a training sample\n",
    "2. Produce h-step-ahead forecasts from the end of that sample\n",
    "3. Compare forecasts against test dataset to compute error rate\n",
    "4. Expand the sample to include the next observation, and repeat\n",
    "\n",
    "Economists sometimes call this a pseudo-out-of-sample forecast evaluation exercise, or time-series cross-validation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will conduct a very simple exercise of this sort using the inflation dataset above. The full dataset contains 203 observations, and for expositional purposes we'll use the first 80% as our training sample and only consider one-step-ahead forecasts."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A single iteration of the above procedure looks like the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:52.173387Z",
     "iopub.status.busy": "2026-07-16T14:25:52.172943Z",
     "iopub.status.idle": "2026-07-16T14:25:52.309465Z",
     "shell.execute_reply": "2026-07-16T14:25:52.303185Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intercept    1.162076\n",
      "ar.L1        0.724242\n",
      "sigma2       5.051600\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Step 1: fit model parameters w/ training sample\n",
    "training_obs = int(len(endog) * 0.8)\n",
    "\n",
    "training_endog = endog[:training_obs]\n",
    "training_mod = sm.tsa.SARIMAX(training_endog, order=(1, 0, 0), trend=\"c\")\n",
    "training_res = training_mod.fit()\n",
    "\n",
    "# Print the estimated parameters\n",
    "print(training_res.params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:52.322370Z",
     "iopub.status.busy": "2026-07-16T14:25:52.322007Z",
     "iopub.status.idle": "2026-07-16T14:25:52.357865Z",
     "shell.execute_reply": "2026-07-16T14:25:52.354254Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        true  forecast    error\n",
      "1999Q3  3.35   2.55262  0.79738\n"
     ]
    }
   ],
   "source": [
    "# Step 2: produce one-step-ahead forecasts\n",
    "fcast = training_res.forecast()\n",
    "\n",
    "# Step 3: compute root mean square forecasting error\n",
    "true = endog.reindex(fcast.index)\n",
    "error = true - fcast\n",
    "\n",
    "# Print out the results\n",
    "print(\n",
    "    pd.concat(\n",
    "        [true.rename(\"true\"), fcast.rename(\"forecast\"), error.rename(\"error\")], axis=1\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To add on another observation, we can use the `append` or `extend` results methods. Either method can produce the same forecasts, but they differ in the other results that are available:\n",
    "\n",
    "- `append` is the more complete method. It always stores results for all training observations, and it optionally allows refitting the model parameters given the new observations (note that the default is *not* to refit the parameters).\n",
    "- `extend` is a faster method that may be useful if the training sample is very large. It *only* stores results for the new observations, and it does not allow refitting the model parameters (i.e. you have to use the parameters estimated on the previous sample).\n",
    "\n",
    "If your training sample is relatively small (less than a few thousand observations, for example) or if you want to compute the best possible forecasts, then you should use the `append` method. However, if that method is infeasible (for example, because you have a very large training sample) or if you are okay with slightly suboptimal forecasts (because the parameter estimates will be slightly stale), then you can consider the `extend` method."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A second iteration, using the `append` method and refitting the parameters, would go as follows (note again that the default for `append` does not refit the parameters, but we have overridden that with the `refit=True` argument):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:52.362499Z",
     "iopub.status.busy": "2026-07-16T14:25:52.362253Z",
     "iopub.status.idle": "2026-07-16T14:25:52.463959Z",
     "shell.execute_reply": "2026-07-16T14:25:52.462850Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "intercept    1.171544\n",
      "ar.L1        0.723152\n",
      "sigma2       5.024580\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Step 1: append a new observation to the sample and refit the parameters\n",
    "append_res = training_res.append(endog[training_obs : training_obs + 1], refit=True)\n",
    "\n",
    "# Print the re-estimated parameters\n",
    "print(append_res.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that these estimated parameters are slightly different than those we originally estimated. With the new results object, `append_res`, we can compute forecasts starting from one observation further than the previous call:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:52.475866Z",
     "iopub.status.busy": "2026-07-16T14:25:52.475602Z",
     "iopub.status.idle": "2026-07-16T14:25:52.513025Z",
     "shell.execute_reply": "2026-07-16T14:25:52.512249Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        true  forecast     error\n",
      "1999Q4  2.85  3.594102 -0.744102\n"
     ]
    }
   ],
   "source": [
    "# Step 2: produce one-step-ahead forecasts\n",
    "fcast = append_res.forecast()\n",
    "\n",
    "# Step 3: compute root mean square forecasting error\n",
    "true = endog.reindex(fcast.index)\n",
    "error = true - fcast\n",
    "\n",
    "# Print out the results\n",
    "print(\n",
    "    pd.concat(\n",
    "        [true.rename(\"true\"), fcast.rename(\"forecast\"), error.rename(\"error\")], axis=1\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Putting it altogether, we can perform the recursive forecast evaluation exercise as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:52.528886Z",
     "iopub.status.busy": "2026-07-16T14:25:52.528633Z",
     "iopub.status.idle": "2026-07-16T14:25:53.429905Z",
     "shell.execute_reply": "2026-07-16T14:25:53.429156Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          1999Q2    1999Q3    1999Q4    2000Q1    2000Q2\n",
      "1999Q3  2.552620       NaN       NaN       NaN       NaN\n",
      "1999Q4  3.010790  3.588286       NaN       NaN       NaN\n",
      "2000Q1  3.342616  3.760863  3.226165       NaN       NaN\n",
      "2000Q2       NaN  3.885850  3.498599  3.885225       NaN\n",
      "2000Q3       NaN       NaN  3.695908  3.975918  4.196649\n"
     ]
    }
   ],
   "source": [
    "# Setup forecasts\n",
    "nforecasts = 3\n",
    "forecasts = {}\n",
    "\n",
    "# Get the number of initial training observations\n",
    "nobs = len(endog)\n",
    "n_init_training = int(nobs * 0.8)\n",
    "\n",
    "# Create model for initial training sample, fit parameters\n",
    "training_endog = endog.iloc[:n_init_training]\n",
    "mod = sm.tsa.SARIMAX(training_endog, order=(1, 0, 0), trend=\"c\")\n",
    "res = mod.fit()\n",
    "\n",
    "# Save initial forecast\n",
    "forecasts[training_endog.index[-1]] = res.forecast(steps=nforecasts)\n",
    "\n",
    "# Step through the rest of the sample\n",
    "for t in range(n_init_training, nobs):\n",
    "    # Update the results by appending the next observation\n",
    "    updated_endog = endog.iloc[t : t + 1]\n",
    "    res = res.append(updated_endog, refit=False)\n",
    "\n",
    "    # Save the new set of forecasts\n",
    "    forecasts[updated_endog.index[0]] = res.forecast(steps=nforecasts)\n",
    "\n",
    "# Combine all forecasts into a dataframe\n",
    "forecasts = pd.concat(forecasts, axis=1)\n",
    "\n",
    "print(forecasts.iloc[:5, :5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have a set of three forecasts made at each point in time from 1999Q2 through 2009Q3. We can construct the forecast errors by subtracting each forecast from the actual value of `endog` at that point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:53.433824Z",
     "iopub.status.busy": "2026-07-16T14:25:53.433545Z",
     "iopub.status.idle": "2026-07-16T14:25:53.495849Z",
     "shell.execute_reply": "2026-07-16T14:25:53.494276Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          1999Q2    1999Q3    1999Q4    2000Q1    2000Q2\n",
      "1999Q3  0.797380       NaN       NaN       NaN       NaN\n",
      "1999Q4 -0.160790 -0.738286       NaN       NaN       NaN\n",
      "2000Q1  0.417384 -0.000863  0.533835       NaN       NaN\n",
      "2000Q2       NaN  0.304150  0.691401  0.304775       NaN\n",
      "2000Q3       NaN       NaN -0.925908 -1.205918 -1.426649\n"
     ]
    }
   ],
   "source": [
    "# Construct the forecast errors\n",
    "forecast_errors = forecasts.apply(lambda column: endog - column).reindex(\n",
    "    forecasts.index\n",
    ")\n",
    "\n",
    "print(forecast_errors.iloc[:5, :5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To evaluate our forecasts, we often want to look at a summary value like the root mean square error. Here we can compute that for each horizon by first flattening the forecast errors so that they are indexed by horizon and then computing the root mean square error fore each horizon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:53.505727Z",
     "iopub.status.busy": "2026-07-16T14:25:53.503086Z",
     "iopub.status.idle": "2026-07-16T14:25:53.552817Z",
     "shell.execute_reply": "2026-07-16T14:25:53.549488Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           1999Q2    1999Q3    1999Q4    2000Q1    2000Q2\n",
      "horizon                                                  \n",
      "1        0.797380 -0.738286  0.533835  0.304775 -1.426649\n",
      "2       -0.160790 -0.000863  0.691401 -1.205918 -0.311464\n",
      "3        0.417384  0.304150 -0.925908 -0.151602 -2.384952\n"
     ]
    }
   ],
   "source": [
    "# Reindex the forecasts by horizon rather than by date\n",
    "def flatten(column):\n",
    "    return column.dropna().reset_index(drop=True)\n",
    "\n",
    "\n",
    "flattened = forecast_errors.apply(flatten)\n",
    "flattened.index = (flattened.index + 1).rename(\"horizon\")\n",
    "\n",
    "print(flattened.iloc[:3, :5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:53.555922Z",
     "iopub.status.busy": "2026-07-16T14:25:53.554973Z",
     "iopub.status.idle": "2026-07-16T14:25:53.569957Z",
     "shell.execute_reply": "2026-07-16T14:25:53.569275Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "horizon\n",
      "1    3.292700\n",
      "2    3.421808\n",
      "3    3.280012\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Compute the root mean square error\n",
    "rmse = (flattened**2).mean(axis=1) ** 0.5\n",
    "\n",
    "print(rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Using `extend`\n",
    "\n",
    "We can check that we get similar forecasts if we instead use the `extend` method, but that they are not exactly the same as when we use `append` with the `refit=True` argument. This is because `extend` does not re-estimate the parameters given the new observation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:53.573052Z",
     "iopub.status.busy": "2026-07-16T14:25:53.572809Z",
     "iopub.status.idle": "2026-07-16T14:25:54.535427Z",
     "shell.execute_reply": "2026-07-16T14:25:54.534061Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          1999Q2    1999Q3    1999Q4    2000Q1    2000Q2\n",
      "1999Q3  2.552620       NaN       NaN       NaN       NaN\n",
      "1999Q4  3.010790  3.588286       NaN       NaN       NaN\n",
      "2000Q1  3.342616  3.760863  3.226165       NaN       NaN\n",
      "2000Q2       NaN  3.885850  3.498599  3.885225       NaN\n",
      "2000Q3       NaN       NaN  3.695908  3.975918  4.196649\n"
     ]
    }
   ],
   "source": [
    "# Setup forecasts\n",
    "nforecasts = 3\n",
    "forecasts = {}\n",
    "\n",
    "# Get the number of initial training observations\n",
    "nobs = len(endog)\n",
    "n_init_training = int(nobs * 0.8)\n",
    "\n",
    "# Create model for initial training sample, fit parameters\n",
    "training_endog = endog.iloc[:n_init_training]\n",
    "mod = sm.tsa.SARIMAX(training_endog, order=(1, 0, 0), trend=\"c\")\n",
    "res = mod.fit()\n",
    "\n",
    "# Save initial forecast\n",
    "forecasts[training_endog.index[-1]] = res.forecast(steps=nforecasts)\n",
    "\n",
    "# Step through the rest of the sample\n",
    "for t in range(n_init_training, nobs):\n",
    "    # Update the results by appending the next observation\n",
    "    updated_endog = endog.iloc[t : t + 1]\n",
    "    res = res.extend(updated_endog)\n",
    "\n",
    "    # Save the new set of forecasts\n",
    "    forecasts[updated_endog.index[0]] = res.forecast(steps=nforecasts)\n",
    "\n",
    "# Combine all forecasts into a dataframe\n",
    "forecasts = pd.concat(forecasts, axis=1)\n",
    "\n",
    "print(forecasts.iloc[:5, :5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:54.538329Z",
     "iopub.status.busy": "2026-07-16T14:25:54.537434Z",
     "iopub.status.idle": "2026-07-16T14:25:54.568557Z",
     "shell.execute_reply": "2026-07-16T14:25:54.567175Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          1999Q2    1999Q3    1999Q4    2000Q1    2000Q2\n",
      "1999Q3  0.797380       NaN       NaN       NaN       NaN\n",
      "1999Q4 -0.160790 -0.738286       NaN       NaN       NaN\n",
      "2000Q1  0.417384 -0.000863  0.533835       NaN       NaN\n",
      "2000Q2       NaN  0.304150  0.691401  0.304775       NaN\n",
      "2000Q3       NaN       NaN -0.925908 -1.205918 -1.426649\n"
     ]
    }
   ],
   "source": [
    "# Construct the forecast errors\n",
    "forecast_errors = forecasts.apply(lambda column: endog - column).reindex(\n",
    "    forecasts.index\n",
    ")\n",
    "\n",
    "print(forecast_errors.iloc[:5, :5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:54.570693Z",
     "iopub.status.busy": "2026-07-16T14:25:54.570491Z",
     "iopub.status.idle": "2026-07-16T14:25:54.617116Z",
     "shell.execute_reply": "2026-07-16T14:25:54.616153Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           1999Q2    1999Q3    1999Q4    2000Q1    2000Q2\n",
      "horizon                                                  \n",
      "1        0.797380 -0.738286  0.533835  0.304775 -1.426649\n",
      "2       -0.160790 -0.000863  0.691401 -1.205918 -0.311464\n",
      "3        0.417384  0.304150 -0.925908 -0.151602 -2.384952\n"
     ]
    }
   ],
   "source": [
    "# Reindex the forecasts by horizon rather than by date\n",
    "def flatten(column):\n",
    "    return column.dropna().reset_index(drop=True)\n",
    "\n",
    "\n",
    "flattened = forecast_errors.apply(flatten)\n",
    "flattened.index = (flattened.index + 1).rename(\"horizon\")\n",
    "\n",
    "print(flattened.iloc[:3, :5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:54.622519Z",
     "iopub.status.busy": "2026-07-16T14:25:54.622269Z",
     "iopub.status.idle": "2026-07-16T14:25:54.635035Z",
     "shell.execute_reply": "2026-07-16T14:25:54.631234Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "horizon\n",
      "1    3.292700\n",
      "2    3.421808\n",
      "3    3.280012\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "# Compute the root mean square error\n",
    "rmse = (flattened**2).mean(axis=1) ** 0.5\n",
    "\n",
    "print(rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By not re-estimating the parameters, our forecasts are slightly worse (the root mean square error is higher at each horizon). However, the process is faster, even with only 200 datapoints. Using the `%%timeit` cell magic on the cells above, we found a runtime of 570ms using `extend` versus 1.7s using `append` with `refit=True`. (Note that using `extend` is also faster than using `append` with `refit=False`)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Indexes\n",
    "\n",
    "Throughout this notebook, we have been making use of Pandas date indexes with an associated frequency. As you can see, this index marks our data as at a quarterly frequency, between 1959Q1 and 2009Q3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:54.637132Z",
     "iopub.status.busy": "2026-07-16T14:25:54.636935Z",
     "iopub.status.idle": "2026-07-16T14:25:54.644450Z",
     "shell.execute_reply": "2026-07-16T14:25:54.643828Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PeriodIndex(['1959Q1', '1959Q2', '1959Q3', '1959Q4', '1960Q1', '1960Q2',\n",
      "             '1960Q3', '1960Q4', '1961Q1', '1961Q2',\n",
      "             ...\n",
      "             '2007Q2', '2007Q3', '2007Q4', '2008Q1', '2008Q2', '2008Q3',\n",
      "             '2008Q4', '2009Q1', '2009Q2', '2009Q3'],\n",
      "            dtype='period[Q-DEC]', length=203)\n"
     ]
    }
   ],
   "source": [
    "print(endog.index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In most cases, if your data has an associated data/time index with a defined frequency (like quarterly, monthly, etc.), then it is best to make sure your data is a Pandas series with the appropriate index. Here are three examples of this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:54.646899Z",
     "iopub.status.busy": "2026-07-16T14:25:54.646695Z",
     "iopub.status.idle": "2026-07-16T14:25:54.657789Z",
     "shell.execute_reply": "2026-07-16T14:25:54.657089Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PeriodIndex(['2000', '2001', '2002', '2003'], dtype='period[Y-DEC]')\n"
     ]
    }
   ],
   "source": [
    "# Annual frequency, using a PeriodIndex\n",
    "index = pd.period_range(start=\"2000\", periods=4, freq=\"Y\")\n",
    "endog1 = pd.Series([1, 2, 3, 4], index=index)\n",
    "print(endog1.index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:54.662175Z",
     "iopub.status.busy": "2026-07-16T14:25:54.661977Z",
     "iopub.status.idle": "2026-07-16T14:25:54.670587Z",
     "shell.execute_reply": "2026-07-16T14:25:54.669820Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DatetimeIndex(['2000-01-01', '2000-04-01', '2000-07-01', '2000-10-01'], dtype='datetime64[us]', freq='QS-JAN')\n"
     ]
    }
   ],
   "source": [
    "# Quarterly frequency, using a DatetimeIndex\n",
    "index = pd.date_range(start=\"2000\", periods=4, freq=\"QS\")\n",
    "endog2 = pd.Series([1, 2, 3, 4], index=index)\n",
    "print(endog2.index)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:54.672975Z",
     "iopub.status.busy": "2026-07-16T14:25:54.672780Z",
     "iopub.status.idle": "2026-07-16T14:25:54.679065Z",
     "shell.execute_reply": "2026-07-16T14:25:54.678493Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DatetimeIndex(['2000-01-31', '2000-02-29', '2000-03-31', '2000-04-30'], dtype='datetime64[us]', freq='ME')\n"
     ]
    }
   ],
   "source": [
    "# Monthly frequency, using a DatetimeIndex\n",
    "index = pd.date_range(start=\"2000\", periods=4, freq=\"ME\")\n",
    "endog3 = pd.Series([1, 2, 3, 4], index=index)\n",
    "print(endog3.index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In fact, if your data has an associated date/time index, it is best to use that even if does not have a defined frequency. An example of that kind of index is as follows - notice that it has `freq=None`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:54.683744Z",
     "iopub.status.busy": "2026-07-16T14:25:54.683543Z",
     "iopub.status.idle": "2026-07-16T14:25:54.693120Z",
     "shell.execute_reply": "2026-07-16T14:25:54.692526Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DatetimeIndex(['2000-01-01 10:08:00', '2000-01-01 11:32:00',\n",
      "               '2000-01-01 17:32:00', '2000-01-02 06:15:00'],\n",
      "              dtype='datetime64[us]', freq=None)\n"
     ]
    }
   ],
   "source": [
    "index = pd.DatetimeIndex(\n",
    "    [\n",
    "        \"2000-01-01 10:08am\",\n",
    "        \"2000-01-01 11:32am\",\n",
    "        \"2000-01-01 5:32pm\",\n",
    "        \"2000-01-02 6:15am\",\n",
    "    ]\n",
    ")\n",
    "endog4 = pd.Series([0.2, 0.5, -0.1, 0.1], index=index)\n",
    "print(endog4.index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can still pass this data to statsmodels' model classes, but you will get the following warning, that no frequency data was found:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:54.698558Z",
     "iopub.status.busy": "2026-07-16T14:25:54.698359Z",
     "iopub.status.idle": "2026-07-16T14:25:54.768573Z",
     "shell.execute_reply": "2026-07-16T14:25:54.762845Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/hostedtoolcache/Python/3.14.6/x64/lib/python3.14/site-packages/statsmodels/tsa/base/tsa_model.py:465: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
      "  self._init_dates(dates, freq)\n",
      "/opt/hostedtoolcache/Python/3.14.6/x64/lib/python3.14/site-packages/statsmodels/tsa/base/tsa_model.py:465: ValueWarning: A date index has been provided, but it has no associated frequency information and so will be ignored when e.g. forecasting.\n",
      "  self._init_dates(dates, freq)\n"
     ]
    }
   ],
   "source": [
    "mod = sm.tsa.SARIMAX(endog4)\n",
    "res = mod.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What this means is that you cannot specify forecasting steps by dates, and the output of the `forecast` and `get_forecast` methods will not have associated dates. The reason is that without a given frequency, there is no way to determine what date each forecast should be assigned to. In the example above, there is no pattern to the date/time stamps of the index, so there is no way to determine what the next date/time should be (should it be in the morning of 2000-01-02? the afternoon? or maybe not until 2000-01-03?).\n",
    "\n",
    "For example, if we forecast one-step-ahead:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:54.771093Z",
     "iopub.status.busy": "2026-07-16T14:25:54.770841Z",
     "iopub.status.idle": "2026-07-16T14:25:54.794281Z",
     "shell.execute_reply": "2026-07-16T14:25:54.788839Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/hostedtoolcache/Python/3.14.6/x64/lib/python3.14/site-packages/statsmodels/tsa/base/tsa_model.py:834: FutureWarning: No supported index is available. In the next version, calling this method in a model without a supported index will result in an exception.\n",
      "  return get_prediction_index(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "4    0.011866\n",
       "dtype: float64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.forecast(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The index associated with the new forecast is `4`, because if the given data had an integer index, that would be the next value. A warning is given letting the user know that the index is not a date/time index.\n",
    "\n",
    "If we try to specify the steps of the forecast using a date, we will get the following exception:\n",
    "\n",
    "    KeyError: 'The `end` argument could not be matched to a location related to the index of the data.'\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-16T14:25:54.796956Z",
     "iopub.status.busy": "2026-07-16T14:25:54.796714Z",
     "iopub.status.idle": "2026-07-16T14:25:54.804706Z",
     "shell.execute_reply": "2026-07-16T14:25:54.803870Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'The `end` argument could not be matched to a location related to the index of the data.'\n"
     ]
    }
   ],
   "source": [
    "# Here we'll catch the exception to prevent printing too much of\n",
    "# the exception trace output in this notebook\n",
    "try:\n",
    "    res.forecast(\"2000-01-03\")\n",
    "except KeyError as e:\n",
    "    print(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ultimately there is nothing wrong with using data that does not have an associated date/time frequency, or even using data that has no index at all, like a Numpy array. However, if you can use a Pandas series with an associated frequency, you'll have more options for specifying your forecasts and get back results with a more useful index."
   ]
  }
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