Numerical distribution functions for seasonal unit root tests

It is often necessary to test for the presence of seasonal unit roots when working with time series data observed at intervals of less than a year. One of the most widely used methods for doing this is based on regressing the seasonal difference of the series over the transformations of the series by applying specific filters for each seasonal frequency. This provides test statistics with non-standard distributions. A generalisation of this method for any periodicity is presented and a response surface regressions approach is used to calculate the P-values of the statistics whatever the periodicity and sample size of the data. The algorithms are prepared with the Gretl open source econometrics package and two empirical examples are presented.