Testing for structural change under non‐stationary variances

Non‐stationarity 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 cumulative sum (CUSUM) related tests for structural change in regression coefficients. Non‐stationary 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.