# The AUTOREG Procedure

The AUTOREG procedure provides regression analysis and forecasting of linear models with autocorrelated or conditional heteroscedastic errors.

The AUTOREG procedure enables you to estimate and predict of linear regression models with autoregressive errors and to test linear hypotheses and estimate and test heteroscedasticity models. Additional features of PROC AUTOREG include

• restrictions on the regression estimates

• optional stepwise selection of autoregressive parameters

• choice of several estimation methods:

• exact maximum likelihood

• exact nonlinear least squares

• Yule-Walker

• iterated Yule-Walker

• forecasts with confidence limits

The AUTOREG procedure offers estimation and forecasting of autoregressive conditional heteroscedasticity (ARCH), generalized autoregressive conditional heteroscedasticity (GARCH), integrated GARCH (I-GARCH), exponential GARCH (E-GARCH), and GARCH-in-mean (GARCH-M) models. Exact gradients are used for GARCH-type model estimation. ARCH and GARCH models can be combined with autoregressive models, with or without regressors.

You can estimate and test heteroscedasticity models, and you can specify the flexible conditional variance from the GARCH model. In addition, you can

• estimate the GARCH model for the conditional t distribution

• estimate various forms of the GARCH-M model

• estimate the GARCH model using the inequality constraints proposed by Nelson and Cao (1992)

• estimate the start-up values for the conditional variance equation

Using PROC AUTOREG, you can test for the stability of the regression coefficients and test for stationarity or unit roots in the time series. You can also specify initial parameter values for GARCH and heteroscedasticity models. Exact gradients are used for GARCH-type model estimation.

The AUTOREG procedure offers a variety of model diagnostic information, including

• autocorrelation plots

• partial autocorrelation plots

• the Durbin-Watson test statistic and significance level and generalized Durbin-Watson tests to any order

• Durbin h and Durbin t statistics and significance levels

• linearized Durbin-Watson test and its marginal probability for the autoregressive model

• Akaike's information criterion

• the Schwarz information criterion

• tests for ARCH errors

• Lagrange multiplier test for serial correlation

• Lagrange multiplier test for heteroscedasticity

• Godfrey LM serial correlation test

• Ramsey's RESET test

• the Jarque-Bera normality test

The AUTOREG procedure also offers embedded missing values.

## Documentation

For further details, see the SAS/ETS® User's Guide