Open Access Open Access  Restricted Access Subscription Access

The Overall Seasonal Integration Tests Under Non-Stationary Alternatives: A Methodological Note

G. El Montasser


Few authors have studied, either asymptotically or in finite samples, the size and power of seasonal unit root tests when the data generating process [DGP] is a non-stationary alternative aside from the seasonal random walk. In this respect, Ghysels, lee and Noh (1994) conducted a simulation study by considering the alternative of a non-seasonal random walk to analyze the size and power properties of some seasonal unit root tests. Analogously, Taylor (2005) completed this analysis by developing the limit theory of statistics of Dickey and Fuller Hasza [DHF] (1984) when the data are generated by a non-seasonal random walk. del Barrio Castro (2007) extended the set of non-stationary alternatives and established, for each one, the asymptotic theory of the statistics subsumed in the HEGY procedure. In this paper, I show that establishing the limit theory of F-type statistics for seasonal unit roots can be debatable in such alternatives. The problem lies in the nature of the regressors that these overall F-type tests specify.


Fisher test, seasonal integration, non-stationary alternatives, Brownian motion, Monte Carlo Simulation.

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.