AUTOREG Procedure

The following new features have been added to the AUTOREG procedure:

• Three asymmetric GARCH models, namely quadratic GARCH, threshold GARCH, and power GARCH, are implemented to measure the impact of news on the future volatility. Power GARCH also considers the long memory property in the volatility.

• Besides the existing two tests for the existence of ARCH effect, Lee and King’s ARCH test and Wong and Li’s ARCH test are implemented. Lee and King’s ARCH test is a one-sided locally most mean powerful (LMMP) test; Wong and Li’s ARCH test is robust to outliers. If the NLAG= option is specified, the statistics based on the final model residuals, along with the OLS residuals, can also be computed.

• The Hannan-Quinn criterion (HQC) is implemented and included in the summary statistics.

• Four statistical tests of independence are implemented: BDS test, runs test, turning point test, and rank version of the von Neumann ratio test. They are powerful tools for model selection and specification test.

• The augmented Dickey-Fuller (ADF) test for unit root is implemented. This test accounts for some form of dependence between the innovations of the time series. The ADF formulation includes lags of the order in the regression. When the lag is specified to be zero, it reduces to the standard Dickey-Fuller Unit root test. In the presence of regressors, the Engle-Granger cointegration test is performed using the augmented Dickey-Fuller test statistic.

• The Elliott-Rothenberg-Stock (ERS) unit root and Ng-Perron (NP) unit root test are implemented. These tests also perform automatic lag length selection by using the information criterion. The Bayesian information criterion (BIC) is used in the ERS test, and the modified Akaike information criterion (AICc) is used in Ng-Perron test.

• The CLASS statement is now supported. A CLASS statement enables you to declare classification variables for use as explanatory effects in a model. When a CLASS variable is used as a predictor in the MODEL statement, the procedure automatically creates a dummy regressor that corresponds to each discrete value or level of the CLASS variable.

• The MODEL statement now supports the use of CLASS variables and interaction terms as predictors.

• The AR, GARCH, and HETERO parameters can be specified in the TEST and RESTRICT statements.

• The likelihood ratio (LR) test and the Lagrange multiplier (LM) test are supported in TEST statement when GARCH= option is specified.