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

This paper is concerned with rolling and recursive regression-based implementations of tests for seasonal unit roots in a univariate time series process. These tests are based on changing subsamples of the data and thus allow one to test the conventional fixed seasonal unit root hypothesis against the alternative that the process under investigation admits a stable autoregressive root over part, if not all, of the sample at either the zero or seasonal frequencies. Asymptotic critical values are provided together with representations for the limiting distributions of these test statistics. A finite sample size and power study of the proposed test statistics is also reported together with a discussion on the problem of lag truncation selection in the context of rolling and recursive test regressions. An application of the proposed test statistics to seasonally unadjusted U.K. consumers’ expenditure on tobacco is considered.