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

TL;DR

This paper examines how a Durbin-Watson pretest influences the coverage probability of confidence intervals in linear regression, providing graphical tools to compare two-stage and always-GFGLS intervals.

Contribution

It introduces new methods for computing coverage probability graphs for confidence intervals based on Durbin-Watson pretesting in regression models.

Findings

Coverage probability graphs help select optimal confidence intervals.

Pretesting affects the coverage properties of confidence intervals.

Tools are provided for any design matrix and parameter of interest.

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.