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

Convert the table DataTable to a timetable:

Clear the row names of DataTable.
Convert the sampling times to a datetime vector.
Convert the table to a timetable by associating the rows with the sampling times in dates.

DataTable.Properties.RowNames = {};
dates = datetime(dates,'ConvertFrom','datenum',...
     'Format','ddMMMyyyy','Locale','en_US');
DataTable = table2timetable(DataTable,'RowTimes',dates);

At the command line, open the Econometric Modeler app.

econometricModeler

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

Import DataTable into the app:

On the Econometric Modeler tab, in the Import section, click .
In the Import Data dialog box, in the Import? column, select the check box for the DataTable variable.
Click Import.

The variables, including PAU, appear in the Data Browser, 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 Data Browser.

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.)

In the Data Browser, select the PAU time series.
On the Econometric Modeler tab, in the Models section, click ARIMA.
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.
Click Estimate.

The model variable ARIMA_PAU appears in the Models section of the Data Browser, and its estimation summary appears in the Model Summary(ARIMA_PAU) document.

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

Documentation