Variance estimation in the change analysis of a linear regression model

We study a ‘direct test’ of Chu and White proposed for detecting changes in the trend of a linear regression model. The power of this test strongly depends on a suitable estimation of the variance of the error variables involved. We discuss various types of variance estimators and derive their asymptotic properties under the null-hypothesis of ‘no change’ as well as under the alternative of ‘a change in linear trend’. A small simulation study illustrates the estimators' finite sample behaviour.