Abstract :
Integration for seasonal time series can take the form of seasonal periodic or nonperiodic
integration+ When seasonal time series are periodically integrated, we
show that any cointegration is either full periodic cointegration or full nonperiodic
cointegration, with no possibility of cointegration applying for only some
seasons+ In contrast, seasonally integrated series can be seasonally, periodically
or nonperiodically cointegrated, with the possibility of cointegration applying for
a subset of seasons+ Cointegration tests are analyzed for periodically integrated
series+ A residual-based test is examined, and its asymptotic distribution is derived
under the null hypothesis of no cointegration+ AMonte Carlo analysis shows good
performance in terms of size and power+ The role of deterministic terms in the
cointegrating test regression is also investigated+ Further, we show that the asymptotic
distribution of the error-correction test for periodic cointegration derived by
Boswijk and Franses ~1995, Review of Economics and Statistics 77, 436– 454!
does not apply for periodically integrated processes+
