A model selection strategy for time series with increasing seasonal variation

We propose a model selection strategy for time series with increasing seasonal variation. This strategy amounts to a selection of the most appropriate differencing filter to obtain a stationary time series without using a Box-Cox transformation. Hence, it is based on a sequence of tests for nonseasonal and seasonal unit roots. Through Monte Carlo replications, we provide new tables of critical values for the various test statistics. We apply our methods, which can be automated, to six example series and find that the results compare favorably to those of an expert.