In this paper, we present tables with critical values for a variety of tests for seasonal and non-seasonal unit roots in seasonal time series. We consider (extensions of) the Hylleberg et al. and Osborn et al. test procedures. These extensions concern time series with increasing seasonal variation and time series with structural breaks in the seasonal means. For each case, we give the appropriate auxiliary test regression, the test statistics, and the corresponding critical values for a selected set of sample sizes. We also illustrate the practical use of the auxiliary regressions for quarterly new car sales in the Netherlands. Supplementary to this paper, we provide Gauss programs with which one can generate critical values for particular seasonal frequencies and sample sizes.

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Keywords mathematical statistics, seasonality, time series analysis
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Journal Journal of Applied Statistics
Franses, Ph.H.B.F, & Hobijn, B. (1997). Critical values for unit root tests in seasonal time series. Journal of Applied Statistics, 25–48. doi:10.1080/02664769723864