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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

  • any order autoregressive or subset autoregressive process

  • 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 of ARCH (autoregressive conditional heteroscedasticity), GARCH (generalized autoregressive conditional heteroscedasticity), I-GARCH (integrated GARCH), E-GARCH (exponential GARCH), and GARCH-M (GARCH in mean) models

  • 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 to any order

    • Durbin h and Durbin t statistics

    • Akaike information criterion

    • Schwarz information criterion

    • tests for ARCH errors

    • Ramsey’s RESET test

    • Chow and PChow tests

    • Phillips-Perron stationarity test

    • CUSUM and CUMSUMSQ statistics

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

  • embedded missing values

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