Introduction

Regression with Autocorrelated and Heteroscedastic Errors

The AUTOREG procedure provides regression analysis and forecasting of linear models with autocorrelated or heteroscedastic errors. The AUTOREG procedure includes the following features:

  • estimation and prediction of linear regression models with autoregressive errors

  • autoregressive or subset autoregressive processes of any order

  • optional stepwise selection of autoregressive parameters

  • choice of the following estimation methods:

    • exact maximum likelihood

    • exact nonlinear least squares

    • Yule-Walker

    • iterated Yule-Walker

  • tests for any linear hypothesis that involves the structural coefficients

  • restrictions for any linear combination of the structural coefficients

  • forecasts with confidence limits

  • estimation and forecasting for A of ARCH (autoregressive conditional heteroscedasticity), and the following variations:

    • GARCH (generalized autoregressive conditional heteroscedasticity)

    • IGARCH (integrated GARCH)

    • EGARCH (exponential GARCH)

    • QGARCH (quadratic GARCH)

    • TGARCH (threshold GARCH)

    • PGARCH (power GARCH)

    • GARCH-M (GARCH-in-mean)

  • combination of ARCH and GARCH models with autoregressive models, with or without regressors

  • estimation and testing of general heteroscedasticity models

  • variety of model diagnostic information, including the following:

    • autocorrelation plots

    • partial autocorrelation plots

    • Durbin-Watson test statistic and generalized Durbin-Watson tests of any order

    • Durbin h and Durbin t statistics

    • Godfrey LM test

    • Ramsey’s RESET test

    • McLeod-Li portmanteau Q test for ARCH disturbances

    • Engle’s LM test for ARCH disturbances

    • Lee and King’s for ARCH disturbances

    • Wong and Li’s test for ARCH disturbances

    • Chow test

    • Bai-Perron supF, UDmaxF, WDmaxF, and supF(l plus 1 vertical-bar l) tests

    • Akaike’s information criterion

    • Schwarz information criterion

    • Phillips-Perron stationarity test

    • Phillips-Ouliaris cointegration test

    • Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test

    • Shin cointegration test

    • augmented Dickey-Fuller test

    • Engle-Granger cointegration test

    • Elliot, Rothenberg, and Stock test

    • Ng and Perron test

    • tests for statistical independence

    • Jarque-Bera test for normality

    • CUSUM and CUMSUMSQ statistics

  • exact significance levels (p-values) for the Durbin-Watson statistic

  • embedded missing values

Last updated: June 19, 2025