Estimate ARIMAX Model Using Econometric Modeler App
This example shows how to specify and estimate an ARIMAX model
using the Econometric Modeler app. The data set, which is stored in
Data_CreditDefaults.mat, contains annual investment-grade
corporate bond default rates, among other predictors, from 1984 through 2004.
Consider modeling corporate bond default rates as a linear, dynamic function of the
other time series in the data set.
Import Data into Econometric Modeler
At the command line, load the
For more details on the data set, enter
Description at the
At the command line, open the Econometric Modeler app.
Alternatively, open the app from the apps gallery (see Econometric Modeler).
DataTimeTable into the app:
On the Econometric Modeler tab, in the Import section, click the Import button .
In the Import Data dialog box, in the Import? column, select the check box for the
The variables, including
IGD, appear in the
Time Series pane, and a time series plot containing all
the series appears in the Time Series Plot(AGE) figure
Assess Stationarity of Dependent Variable
In the Time Series pane, double-click
IGD. The value of
appears in the Preview pane, and a time series plot for
IGD appears in the Time Series
Plot(IGD) figure window.
IGD appears to be stationary.
IGD has a unit root by conducting a
On the Econometric Modeler tab, in the Tests section, click New Test > Phillips-Perron Test.
On the PP tab, in the Parameters section, set Number of Lags to
In the Tests section, click Run Test.
The test results in the Results table of the PP(IGD) document.
The test rejects the null hypothesis that
contains a unit root.
Inspect Correlation and Collinearity Among Variables
Plot the pairwise correlations between variables.
Select all variables in the Time Series pane by clicking
AGE, then press Shift and click
Click the Plots tab, then click Correlations.
A correlations plot appears in the Correlations(AGE) figure window.
All predictors appear weakly associated with
You can test whether the correlation coefficients are significant by using
corrplot at the command line.
Assess whether any variables are collinear by performing Belsley collinearity diagnostics:
In the Time Series pane, select all variables.
Click the Econometric Modeler tab. Then, in the Tests section, click New Test > Belsley Collinearity Diagnostics.
Tabular results appear in the Collinearity(AGE) document.
None of the condition indices are greater than the condition-index tolerance
30). Therefore, the variables do not exhibit
Specify and Estimate ARIMAX Model
Consider an ARIMAX(0,0,1) model for
all predictors. Specify and estimate the model.
In the Time Series pane, click
Click the Econometric Modeler tab. Then, in the Models section, click the arrow to display the models gallery.
In the models gallery, in the ARMA/ARIMA Models section, click ARIMAX.
In the ARIMAX Model Parameters dialog box, on the Lag Order tab, set Moving Average Order to
In the Predictors section, select the Include? check box for each time series.
Click Estimate. The model variable
ARIMAX_IGDappears in the Models pane, its value appears in the Preview pane, and its estimation summary appears in the Model Summary(ARIMAX_IGD) document.
At a 0.10 significance level, all predictors and the MA coefficient are significant.
Close all figure windows and documents.
Check Goodness of Fit
Check that the residuals are normally distributed and uncorrelated by plotting a histogram, quantile-quantile plot, and ACF of the residuals.
In the Models pane, select
On the Econometric Modeler tab, in the Diagnostics section, click Residual Diagnostics > Residual Histogram.
Click Residual Diagnostics > Residual Q-Q Plot.
Click Residual Diagnostics > Autocorrelation Function.
In the right pane, drag the Histogram(ARIMAX_IGD) and QQPlot(ARIMAX_IGD) figure windows so that they occupy the upper two quadrants, and drag the ACF so that it occupies the lower two quadrants.
The residual histogram and quantile-quantile plots suggest that the residuals might not be normally distributed. According to the ACF plot, the residuals do not exhibit serial correlation. Standard inferences rely on the normality of the residuals. To remedy nonnormality, you can try transforming the response, then estimating the model using the transformed response.