A Random Forest-based Approach to Combining and Ranking Seasonality Tests

Virtually every seasonal adjustment software includes an ensemble of tests for assessing whether a given time series is in fact seasonal and hence a candidate for seasonal adjustment. However, such tests are certain to produce either agreeing or conflicting results, raising the questions how to identify the most accurate tests and how to aggregate the results in the latter case. We suggest a novel random forest-based approach to answer these questions. We simulate seasonal and non-seasonal ARIMA processes that are representative of the macroeconomic time series analysed regularly by the Bundesbank. Treating the time series’ seasonal status as a classification problem, we use the p-values of the seasonality tests implemented in the seasonal adjustment software JDemetra+ as predictors to train conditional random forests on the simulated data. We show that this aggregation approach avoids the size distortions of the JDemetra+ tests without sacrificing too much power compared to the most powerful test. We also find that the modified QS and Friedman tests are the most accurate ones in the considered ensemble.