Shrinkage estimators of time series seasonal factors and their effect on forecasting accuracy

This paper shows that forecasting accuracy can be improved through better estimation of seasonal factors under conditions for which relatively simple methods are preferred, such as relatively few historical data, noisy data, and/or a large number of series to be forecast. In such situations, the preferred method of seasonal adjustment is often ratio-to-moving-averages (classical) decomposition. This paper proposes two shrinkage estimators to improve the accuracy of classical decomposition seasonal factors. In a simulation study, both of the proposed estimators provided consistently greater accuracy than classical decomposition, with the improvement sometimes being dramatic. The performances of the two estimators depended on characteristics of the series, and guidelines were developed for choosing one of them under a given set of conditions. For a set of monthly, M-competition series, greater forecasting accuracy was achieved when either of the proposed methods was used for seasonal adjustment rather than classical decomposition, and the greatest accuracy was achieved by following the guidelines for choosing a method.