TESTING STRICT STATIONARITY WITH APPLICATIONS TO MACROECONOMIC TIME SERIES

We propose a model-free test for strict stationarity. The idea is to estimate a nonparametric time-varying characteristic function and compare it with the empirical characteristic function based on the whole sample. We also propose several derivative tests to check time-invariant moments, weak stationarity, and pth order stationarity. Monte Carlo studies demonstrate excellent power of our tests. We apply our tests to various macroeconomic time series and find overwhelming evidence against strict and weak stationarity for both level and first-differenced series. This suggests that the conventional time series econometric modeling strategies may have room to be improved by accommodating these time-varying features.