Damping seasonal factors: Shrinkage estimators for the X-12-ARIMA program

We examine the effect of damping X-12-ARIMA's estimated seasonal variation on the accuracy of its seasonal adjustments of time series. Two methods for damping seasonals are proposed. In a simulation experiment, we generated time series data for each of 90 distinct experimental conditions that, in aggregate, characterize the variety of monthly series in the M3-competition. X-12-ARIMA consistently overestimated the actual seasonal variation by an amount consistent with statistical theory. Damping seasonals reduced X-12-ARIMA's estimation error by as much as 79% and under no conditions was estimation error increased beyond a trivial amount. Improvement depended primarily on the degree to which random variation in a series dominated seasonal variation. When the multiplicative X-12-ARIMA model did not match the data-generating model, overestimation was less for trend series than for series with no trend; otherwise the presence of trend had no discernible effect. One of the proposed methods was somewhat more accurate and robust, but more complex, than the other. In an analysis of real data—the 1428 monthly series of the M3-competition-damping X-12-ARIMA seasonals prior to forecasting (1) reduced the average forecasting MAPE by 4.9–1.4% and (2) improved forecasting accuracy for 59–65% of the series, depending on the forecasting horizon. This research suggests that damping X-12-ARIMA seasonals leads to more accurate seasonal adjustments of time series, thus providing a more reliable basis for policy-making, forecasting, and the evaluation of forecasting methods by researchers.