Construction of Confidence Sets for the Break Date in Regression Models with Non-homogeneous Regressors

Abstract

This paper proposes constructing the confidence sets for the break date in linear regression models with non-homogeneous regressors. We first derive optimal tests for the location of the break date and then construct the confidence sets by inverting the tests. It turns out that, in general, the asymptotic distributions of the test statistics for the location of the break date depend on nuisance parameters, the moments of the non-homogeneous regressors, but we propose the solution to this problem when a linear trend is only the non-homogeneous regressor. The method proposed in the paper works well in finite samples in that the empirical coverage rates are close to the nominal confidence level and thus our method is practically useful.