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Specify t Innovation Distribution Using Econometric Modeler App

This example shows how to specify a t innovation distribution for an ARIMA model by using the Econometric Modeler app. The example also shows how to fit the model to data. The data set, which is stored in Data_JAustralian.mat, contains the log quarterly Australian Consumer Price Index (CPI) measured from 1972 and 1991, among other time series.

Import Data into Econometric Modeler

At the command line, load the Data_JAustralian.mat data set.

load Data_JAustralian

At the command line, open the Econometric Modeler app.


Alternatively, open the app from the apps gallery (see Econometric Modeler).

Import DataTimeTable into the app:

  1. On the Econometric Modeler tab, in the Import section, click the Import button .

  2. In the Import Data dialog box, in the Import? column, select the check box for the DataTimeTable variable.

  3. Click Import.

The variables, including PAU, appear in the Time Series pane, and a time series plot containing all the series appears in the Time Series Plot(EXCH) figure window.

Create a time series plot of PAU by double-clicking PAU in the Time Series pane.

This screen shot shows a time series plot of the variable PAU where the x axis shows a time period from 1972 through the early 1990's.

Specify and Estimate ARIMA Model

Estimate an ARIMA(2,1,0) model for the log quarterly Australian CPI. Specify a t innovation distribution. (For details, see Implement Box-Jenkins Model Selection and Estimation Using Econometric Modeler App and Perform ARIMA Model Residual Diagnostics Using Econometric Modeler App.)

  1. In the Time Series pane, select the PAU time series.

  2. On the Econometric Modeler tab, in the Models section, click ARIMA.

  3. In the ARIMA Model Parameters dialog box, on the Lag Order tab:

    1. Set the Degree of Integration to 1.

    2. Set the Autoregressive Order to 2.

    3. Click the Innovation Distribution button, then select t.

      ARIMA Model Parameters dialog box with the Lag order tab selected. Autoregressive Order is set to 2, Degree of Integration is set to 1, Moving Average Order is set to zero, and the check box next to "Include Constant Term" is selected. A model equation section is below the given parameters. The "Details", "Estimate" and "Cancel" buttons are at the bottom right side of the dialog box, below the equation.

  4. Click Estimate.

The model variable ARIMA_PAU appears in the Models pane, its value appears in the Preview pane, and its estimation summary appears in the Model Summary(ARIMA_PAU) document.

This screen shot shows time series plots of Model Fit for PAU and ARIMA_PAU and Residual Plot for the variable ARIMA_PAU on the left and two tables for Parameters and Goodness of Fit to the right.

The app estimates the t innovation degrees of freedom (DoF) along with the model coefficients and variance.

See Also




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