Chapter 8

The AUTOREG Procedure

Chapter Table of Contents
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 GETTING STARTED . . . . . . . . . . . Regression with Autocorrelated Errors . . Forecasting Autoregressive Error Models Testing for Autocorrelation . . . . . . . . Stepwise Autoregression . . . . . . . . . Testing for Heteroscedasticity . . . . . . Heteroscedasticity and GARCH Models . SYNTAX . . . . . . . . . . . Functional Summary . . . . PROC AUTOREG Statement BY Statement . . . . . . . . MODEL Statement . . . . . HETERO Statement . . . . . RESTRICT Statement . . . TEST Statement . . . . . . . OUTPUT Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 305 311 313 315 317 320 324 324 327 328 328 335 337 338 339 342 342 342 346 347 352 354 358 363 366 367 368 368

DETAILS . . . . . . . . . . . . . . . . . . . . . . . . . . Missing Values . . . . . . . . . . . . . . . . . . . . . . Autoregressive Error Model . . . . . . . . . . . . . . . Alternative Autocorrelation Correction Methods . . . . . GARCH, IGARCH, EGARCH, and GARCH-M Models R2 Statistics and Other Measures of Fit . . . . . . . . . Generalized Durbin-Watson Tests . . . . . . . . . . . . Testing . . . . . . . . . . . . . . . . . . . . . . . . . . Predicted Values . . . . . . . . . . . . . . . . . . . . . OUT= Data Set . . . . . . . . . . . . . . . . . . . . . . OUTEST= Data Set . . . . . . . . . . . . . . . . . . . . Printed Output . . . . . . . . . . . . . . . . . . . . . . . ODS Table Names . . . . . . . . . . . . . . . . . . . .

EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 Example 8.1 Analysis of Real Output Series . . . . . . . . . . . . . . . . . . 370 301

Part 2. General Information
Example 8.2 Comparing Estimates and Models Example 8.3 Lack of Fit Study . . . . . . . . . Example 8.4 Missing Values . . . . . . . . . . Example 8.5 Money Demand Model . . . . . . Example 8.6 Estimation of ARCH(2) Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 377 380 384 387

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392

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Chapter 8

The AUTOREG Procedure
Overview
The AUTOREG procedure estimates and forecasts linear regression models for time series data when the errors are autocorrelated or heteroscedastic. The autoregressive error model is used to correct for autocorrelation, and the generalized autoregressive conditional heteroscedasticity (GARCH) model and its variants are used to model and correct for heteroscedasticity. When time series data are used in regression analysis, often the error term is not independent through time. Instead, the errors are serially correlated or autocorrelated. If the error term is autocorrelated, the efficiency of ordinary least-squares (OLS) parameter estimates is adversely