Testing for a Moderately Explosive Process with Structural Change in Drift*

Abstract

AbstractThis paper studies large sample properties of a moderately explosive autoregression with a structural change in the unobservable drift term, and develops asymptotic tests for the null of moderate explosiveness under different dependence structures. When the innovation sequence is independently and identically distributed (i.i.d.), we show that the t statistic is asymptotically standard normal. When the innovations are weakly dependent in the form of homoskedasticity or conditional heteroskedasticity, we invoke the fixed‐smoothing asymptotics to construct the heteroskedasticity and autocorrelation robust standard error, under which the t statistic follows Student’s t distribution in large samples. Monte Carlo simulations show that our tests have small size distortion and high power in finite samples. As we impose no restrictions on the occurrence time and magnitude of the drift, our proposed asymptotic tests enjoy strong robustness and applicability.