The effect of a Durbin-Watson pretest on confidence intervals in regression

Abstract

Consider a linear regression model and suppose that our aim is to find a confidence interval for a specified linear combination of the regression parameters. In practice, it is common to perform a Durbin-Watson pretest of the null hypothesis of zero first-order autocorrelation of the random errors against the alternative hypothesis of positive first-order autocorrelation. If this null hypothesis is accepted then the confidence interval centred on the Ordinary Least Squares estimator is used; otherwise the confidence interval centred on the Feasible Generalized Least Squares estimator is used. We provide new tools for the computation, for any given design matrix and parameter of interest, of graphs of the coverage probability functions of the confidence interval resulting from this two-stage procedure and the confidence interval that is always centred on the Feasible Generalized Least Squares estimator. These graphs are used to choose the better confidence interval, prior to any examination of the observed response vector.