Testing for Structural Change Under Nonstationary Variances

Nonstationarity of the volatility process reflects low-frequency volatility changes of an economic time series, and its theoretical and empirical relevance has been widely recognized. We investigate how it affects CUSUM-related tests for structural change in regression coefficients. Nonstationary variances generally invalidate standard structural change tests by introducing an infinite-dimensional nuisance parameter in the limit distribution, and we propose robust alternatives. We also show that the practical relevance of the non-monotonic power issue which is peculiarly associated with the test for changing mean, is mitigated (although the power against a small change is reduced) if there is comparable change in volatility levels. The results are useful to validate/modify a test to ensure monotonic power. Simulations and an empirical example provide finite-sample evidence of the theoretical findings