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 series.
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.
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 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:
Set the Degree of Integration to
1
.
Set the Autoregressive Order to
2
.
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.
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.
Visually assess whether the residuals are normally distributed by plotting their histogram and a quantile-quantile plot:
Close the Model Summary(ARIMA_PAU) document.
With ARIMA_PAU
selected in the
Data Browser, 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 Data Browser, in the Diagnostics
section, click Residual Diagnostics >
Autocorrelation Function.
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 ARIMA_PAU
selected in the Data Browser, click the
Econometric Modeler tab. Then, click the
Diagnostics section, click Residual
Diagnostics > Squared Residual
Autocorrelation.
Significant autocorrelations occur at lags 4 and 5, which suggests a composite
conditional mean and variance model for PAU
.