The seasonal KPSS Test: some extensions and further results

The literature distinguishes finite sample studies of seasonal stationarity quite less intensely than it shows for seasonal unit root tests. Therefore, the use of both types of tests for better exploring time series dynamics is seldom noticed in the relative studies on such a topic. Recently, Lyhagen (2006) introduced for quarterly data the seasonal KPSS test which null hypothesis is no seasonal unit roots. In the same manner, as most unit root limit theory, the asymptotic theory of the seasonal KPSS test depends on whether the data has been filtered by a preliminary regression. More specifically, one may proceed to the extraction of deterministic components – such as the mean and trend – from the data before testing. In this paper, I took account of de-trending on the seasonal KPSS test. A sketch of its limit theory was provided in this case. Also, I studied in finite sample the behaviour of the test for monthly time series. This could enrich our knowledge about it since it was – as I mentioned above – early introduced for quarterly data. Overall, the obtained results showed that the seasonal KPSS test preserved its good size and power properties. Furthermore, like the test of Kwiatkowski et al. [KPSS] (1992), the nonparametric corrections of residual variances may smooth the wide variations of the seasonal KPSS empirical sizes.