A Mean Squared Error Criterion for Comparing X-12-ARIMA and Model-Based Seasonal Adjustment Filters

Various authors — Cleveland and Tiao (1976), Burridge and Wallis (1984), and Depoutot and Planas (1998) — have compared weight functions from X-11 versus model-based seasonal adjustment filters. We suggest a different approach to comparing filters by computing the mean squared error (MSE) when using an X-12-ARIMA filter for estimating the underlying seasonal component from an ARIMA model-based decomposition, and comparing this to the MSE of the optimal model-based estimator. This provides a criterion for choosing an X-12 filter for a given series (model the series and pick the X-12 filter with lowest MSE), and also provides results on how much MSE increases when using an X-12 filter rather than the optimal model-based filter. Calculations for monthly time series following the airline model with various parameter values show little increase in MSE for estimating the canonical seasonal component by using the best X-12 filter instead of the optimal model-based filter, particularly for concurrent adjustment. The results are much less favorable to the X12 filters with a uniform prior distribution on the white noise allocation in the seasonal model decomposition. Examinations of simulated series show that, for the canonical decomposition, automatic filter choices of the X-12-ARIMA program sometimes use shorter seasonal moving averages than is desirable.

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