Powerful Tests of Structural Change That are Robust to Strong Serial Correlation

Abstract

This paper proposes powerful and serial correlation robust test statistics that can be used to test for the presence of structural change in the trend function of a univariate time series. Four models are analyzed, each model corresponding to a different way in which a trend break might occur. Given a model, the proposed tests are designed to detect a single break at an unknown date. The tests do not require the knowledge of the form of serial correlation in the data, and they are made robust to the presence of highly persistent serial correlation and a unit root in the errors by using a more comprehensive version of the scaling factor approach of Vogelsang (1998b). The tests utilize the popular nonparametric kernel variance estimators. The fixed-bandwidth asymptotic framework, proposed by Kiefer and Vogelsang (2003), is used to approximate the effects of the variance estimators on the test statistics. The fixed-bandwidth framework makes possible the choice of kernel and bandwidth that deliver tests with maximal asymptotic power within a specific class of tests. For each of the proposed tests, concrete and specific recommendations are made for the bandwidth and kernel to be used in practice. The recommended tests are shown to have good finite sample size and power properties.