Perform ARIMA Model Residual Diagnostics Using Econometric Modeler App
This example shows how to evaluate ARIMA model assumptions by
performing residual diagnostics in the Econometric Modeler app. 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
Import Data into Econometric Modeler
At the command line, load 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
PAU, appear in the
Time Series pane, and a time series plot containing all
the series appears in the Time Series Plot(EXCH) figure
Create a time series plot of
PAU by double-clicking
PAU in the Time Series
Specify and Estimate ARIMA Model
Estimate an ARIMA(2,1,0) model for the log quarterly Australian CPI (for details, see Implement Box-Jenkins Model Selection and Estimation Using Econometric Modeler App).
In the Time Series pane, select the
On the Econometric Modeler tab, in the Models section, click ARIMA.
In the ARIMA Model Parameters dialog box, on the Lag Order tab:
Set the Degree of Integration to
Set the Autoregressive Order to
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.
In the Model Summary(ARIMA_PAU) document, the Residual Plot figure is a time series plot of the residuals. The plot suggests that the residuals are centered at y = 0 and they exhibit volatility clustering.
Perform Residual Diagnostics
Visually assess whether the residuals are normally distributed by plotting their histogram and a quantile-quantile plot:
Close the Model Summary(ARIMA_PAU) document.
ARIMA_PAUselected in the Models pane, on the Econometric Modeler tab, in the Diagnostics section, click Residual Diagnostics > Residual Histogram.
Click Residual Diagnostics > Residual Q-Q Plot.
Inspect the histogram by clicking the Histogram(ARIMA_PAU) figure window.
Inspect the quantile-quantile plot by clicking the QQPlot(ARIMA_PAU) figure window.
The residuals appear approximately normally distributed. However, there is an excess of large residuals, which indicates that a t innovation distribution might be a reasonable model modification.
Visually assess whether the residuals are serially correlated by plotting
their autocorrelations. With
ARIMA_PAU selected in
the Models pane, in the Diagnostics
section, click Residual Diagnostics >
All lags that are greater than 0 correspond to insignificant autocorrelations. Therefore, the residuals are uncorrelated in time.
Visually assess whether the residuals exhibit heteroscedasticity by plotting
the ACF of the squared residuals. With
selected in the Models pane, click the
Econometric Modeler tab. Then, click the
Diagnostics section, click Residual
Diagnostics > Squared Residual
Significant autocorrelations occur at lags 4 and 5, which suggests a composite
conditional mean and variance model for
- Infer Residuals for Diagnostic Checking
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