Likelihood ratio tests for seasonal unit roots (Q2703247)

The authors consider tests for seasonal unit roots in univariate time series processes; i.e., whether or not the data generating process (DGP) for the variable of interest admits unit roots at zero, bi-annual and other seasonal frequencies. However, in the spirit of \textit{D.A. Dickey} and \textit{W.A. Fuller} [Econometrica 49, 1057-1072 (1981; Zbl 0471.62090)] the point of departure from earlier contributions is that it fully incorporates the restrictions on the deterministics of the DGP implied by the presence of seasonal unit roots.NEWLINENEWLINENEWLINERegression-based tests for seasonal unit roots in a general seasonal context as separate likelihood ratio or \(F\) tests for unit roots at the zero, bi-annual and other seasonal frequencies are developed. Different specifications of the deterministics are considered which allow for the possibilities of an intercept or seasonal intercepts together with a time-trend variable or seasonal time-trend variables. This analysis also permits the derivation of representations for the limiting distributions of the pertinent statistics in this and other scenarios for the deterministics. The seasonal unit root properties of the logarithm of monthly seasonally unadjusted real industrial production in Canada are re-examined.