  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.

Methodology