Testing for Stationarity in the Frequency Domain Using a Sphericity Statistic

Non-stationary time series are common in practice and distinguishing them from stationary series has important implications for estimation, identification and forecasting as stationarity models often lead to simpler solutions. We develop a statistical test for stationarity based on the ratio of the arithmetic to geometric means of spectra obtained from non-overlapping segments of the time series. The power of this test is compared to one of the most well-known tests in time series analysis, the KPSS test. Results indicate that the proposed test can replace the KPSS test, particularly for time-varying AR models where it significantly outperforms the current standard