A likelihood-ratio test for seasonal unit roots

A new test for the presence of seasonal unit roots in a quarterly time series, i.e. for seasonal integratedness, is constructed. a seasonally integrated process is characterized by a factor 1-l4 in its autoregressive representation. the test is based on the correlation between the series xt and its seasonal differences xt- xt-4, adjusted for lagged differences. it is equivalent to the likelihood-ratio test against stationary alternatives. if the series is taken from a seasonally integrated process indeed, the test statistic can be shown to converge towards a limit distribution. fractiles of this distribution are given and finite-sample properties are studied via monte carlo. the use of correlations instead of second-order cross-moments around zero imposes a non-trivial bias whose influence is seen from simulations. if the series is stationary, a random walk, contains additional unit roots, or can be stationarized by seasonal moving averages, the test statistic can be shown todiverge.