Non-parametric testing for seasonally and periodically integrated processes

This article obtains the asymptotic distributions of the seasonal variance ratio tests proposed by A.M.R. Taylor (2005, 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, 108, 343) for the original (non-seasonal) variance ratio test. The multivariate non-parametric cointegration test of Breitung (2002 ) 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.