Temporally aggregating models to improve the accuracy of seasonal M3 forecasts

This is a study of forecasting models that aggregate monthly times series into bimonthly and quarterly models using the 1,428 seasonal monthly series of the M3 competition of Makridakis and Hibon (2000). These aggregating models are used to answer the question of whether aggregation models of monthly time series significantly improve forecast accuracy. Through aggregation, the forecast mean absolute deviations (MADs) and mean absolute percent errors (MAPEs) were found to be statistically significantly lower at a 0.001 level of significance. In addition, the ratio of the forecast MAD to the best forecast model MAD was reduced from 1.066 to 1.0584. While those appear to be modest improvements, a reduction in the MAD affects a forecasting horizon of 18 months for 1,428 time series, thus the absolute deviations of 25,704 forecasts (i.e., 18*1,428 series) were reduced. Similar improvements were found for the symmetric MAPE.