Recursive and rolling regression-based tests of the seasonal unit root hypothesis

This paper is concerned with rolling and recursive regression-based impleme ntations of tests for seasonal unit roots in a univariate time series proce ss. These tests are based on changing subsamples of the data and thus allow one to test the conventional fixed seasonal unit root hypothesis against t he alternative that the process under investigation admits a stable autoreg ressive root over part, if not all, of the sample at either the zero or sea sonal frequencies. Asymptotic critical values are provided together with re presentations for the limiting distributions of these test statistics. A fi nite sample size and power study of the proposed test statistics is also re ported together with a discussion on the problem of lag truncation selectio n in the context of rolling and recursive test regressions. An application of the proposed test statistics to seasonally unadjusted U.K. consumers' ex penditure on tobacco is considered. (C) 2001 Elsevier Science S.A. All righ ts reserved.