Joint change point estimation in regression coeffcients and variances of the errors of a linear model

This paper describes how to estimate the alternative model that admits a one-time break in coeffcients of a linear regression function and variances of the errors. Bai and Perron (1998) introduced an estimation and testing procedure for multiple breaks in regression coeffcients. We limit the number of breaks to one but extend the estimation to the alternative model that allows for variances of the errors to break too. The method is based on application of specific objective functions in conjunction with the tests ofstructural change. In particular, sup-Wald test of Andrews (1993) can be used to detect structural breaks. Andrews and Ploberger (1994) introduce optimal tests of constancy of model parameters when the change point is unknown. However, these tests lose their power optimality properties when the break happens in both the mean and the variance of a process. For such an alternative we introduce a statistic with a modified measure of a distance between model parameters before and after the break. In a Monte-Carlo experiment we show that the power of the corresponding sup-test dominates that of the sup-Wald test. If a change point is known, then the test based on this statistic is uniformly more powerful than the Wald test.