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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 inData_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 theData_CreditDefaults.matdata set.

loadData_CreditDefaults

For more details on the data set, enterDescriptionat the command line.

Convert the tableDataTableto a timetable:

  1. Clear the row names ofDataTable.

  2. Convert the sampling years to adatetimevector.

  3. Convert the table to a timetable by associating the rows with the sampling times indates.

DataTable.Properties.RowNames = {}; dates = datetime(dates,12,31,'Format','yyyy'); DataTable = table2timetable(DataTable,'RowTimes',dates);

At the command line, open theEconometric Modeler应用程序。

econometricModeler

Alternatively, open the app from the apps gallery (seeEconometric Modeler)。

ImportDataTableinto the app:

  1. On theEconometric Modelertab, in theImportsection, click.

  2. In theImport Datadialog box, in theImport?column, select the check box for theDataTablevariable.

  3. ClickImport.

The variables, includingIGD, appear in theTime Seriespane, and a time series plot containing all the series appears in theTime Series Plot(AGE)figure window.

Assess Stationarity of Dependent Variable

In theTime Seriespane, double-clickIGD. The value ofIGDappears in thePreviewpane, and a time series plot forIGDappears in theTime Series Plot(IGD)figure window.

IGDappears to be stationary.

Assess whetherIGDhas a unit root by conducting a Phillips-Perron test:

  1. On theEconometric Modelertab, in theTestssection, clickNew Test>Phillips-Perron Test.

  2. On the页tab, in theParameterssection, setNumber of Lagsto1.

  3. In theTestssection, clickRun Test.

The test results in theResultstable of the页(IGD)document.

The test rejects the null hypothesis thatIGDcontains a unit root.

Inspect Correlation and Collinearity Among Variables

Plot the pairwise correlations between variables.

  1. Select all variables in theTime Seriespane by clickingAGE, then pressShiftand clickSPR.

  2. Click thePlotstab, then clickCorrelations.

A correlations plot appears in theCorrelations(AGE)figure window.

All predictors appear weakly associated withIGD. You can test whether the correlation coefficients are significant by usingcorrplotat the command line.

Assess whether any variables are collinear by performing Belsley collinearity diagnostics:

  1. In theTime Seriespane, select all variables.

  2. Click theEconometric Modelertab. Then, in theTestssection, clickNew Test>Belsley Collinearity Diagnostics.

Tabular results appear in theCollinearity(AGE)document.

None of the condition indices are greater than the condition-index tolerance (30)。因此,没有表现出明显的变量multicollinearity.

Specify and Estimate ARIMAX Model

Consider an ARIMAX(0,0,1) model forIGDcontaining all predictors. Specify and estimate the model.

  1. In theTime Seriespane, clickIGD.

  2. Click theEconometric Modelertab. Then, in theModelssection, click the arrow to display the models gallery.

  3. In the models gallery, in theARMA/ARIMA Modelssection, clickARIMAX.

  4. In theARIMAX Model Parametersdialog box, on theLag Ordertab, setMoving Average Orderto1.

  5. In thePredictorssection, select theInclude?check box for each time series.

  6. ClickEstimate. The model variableARIMAX_IGDappears in theModelspane, its value appears in thePreviewpane, and its estimation summary appears in theModel 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.

  1. In theModelspane, selectARIMAX_IGD.

  2. On theEconometric Modelertab, in theDiagnosticssection, clickResidual Diagnostics>Residual Histogram.

  3. ClickResidual Diagnostics>Residual Q-Q Plot.

  4. ClickResidual Diagnostics>Autocorrelation Function.

  5. In the right pane, drag theHistogram(ARIMAX_IGD)andQQPlot(ARIMAX_IGD)图窗口,这样他们占领上两个问uadrants, 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.

See Also

Apps

Objects

Functions

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