Non-parametric testing for seasonally and periodically integrated processes


Tomás del Barrio Castro, Applied Economics, Gaspar Melchor de Jovellanos Building, Campus UIB University of the Balearic, Islands Ctra. Valldelmosa Km 7,5., 7122 Balearic Islands, Spain.


This article obtains the asymptotic distributions of the seasonal variance ratio tests proposed by A.M.R. Taylor (2005,Journal of Econometrics 124, 33) when these tests are applied to a periodically integrated process [PI(1)]. In contrast to the situation where the process is seasonally integrated [SI(1)], all test statistics in the PI(1) case are driven by a single stochastic trend and hence follow the distribution obtained by Breitung (2002, Journal of Econometrics 108, 343) for the original (non-seasonal) variance ratio test. The multivariate non-parametric cointegration test of Breitung (2002 Journal of Econometrics 108, 343) is also investigated to distinguish between PI and SI processes. A Monte Carlo analysis shows how these results apply in finite samples for both SI and PI processes and an empirical application investigates seasonally unadjusted quarterly US industrial production series.