The Seasonal KPSS Test with Deterministic Seasonality

Abstract

In this paper, we establish the limit theory of the seasonal KPSS test [The seasonal KPSS statistic, Econom. Bull. 3 (2006), pp. 1-9] under the null by involving seasonal dummies. Taking these variables into account can be advantageous through different levels. On the one hand, the seasonal KPSS test can be interpreted as a test of deterministic seasonality. Moreover, it could be used complementarily with seasonal unit root tests to analyse rigorously the dynamic properties of time series. On the other hand, the inclusion of seasonal dummies provides the test with an explicit model based regression that constitutes in itself a compulsory support for its limit theory.