Rescaled variance tests for seasonal stationarity

Abstract

This paper introduces rescaled variance [V/S] tests for seasonal stationarity. The V/S statistic is designed by Giraitis, L., P. Kokoszka, R. Leipus, and G. Teyssière. 2003. “Rescaled Variance and Related Tests for Long Memory in Volatility and Levels.” Journal of Econometrics 112: 265–94 to be the mean corrected versions of the KPSS statistic. In the seasonal context, Canova, F., and B. E. Hansen. 1995. “Are Seasonal Patterns Constant over Time? A Test for Seasonal Stability.” Journal of Business & Economic Statistics 13: 237–52 present the seasonal generalization of the KPSS statistic. In this regard, I aim to strengthen the work of Canova, F., and B. E. Hansen. 1995. “Are Seasonal Patterns Constant over Time? A Test for Seasonal Stability.” Journal of Business & Economic Statistics 13: 237–52 [CH] by mean correction in the seasonal framework. I obtain the asymptotic distributions of the seasonal V/S tests. The V/S tests enjoy better power performance than the CH tests while exhibiting similiar size performance. Furthermore, by data pre-filtering, I propose robustified versions of the V/S statistics to eliminate the unattended unit root problem observed in the CH tests.