Generalised Estimators for Seasonal Forecasting by Combining Grouping with Shrinkage Approaches


Correspondence to: Kui Zhang, Centre of OR and Applied Statistics, University of Salford, Salford M5 4WT, UK.



In this paper, generalised estimators are proposed to estimate seasonal indices for certain forms of additive and mixed seasonality. The estimators combine one of two group seasonal indices methods—Dalhart's group method and Withycombe's group method—with a shrinkage method in different ways. Optimal shrinkage parameters are derived to maximise the performance of the estimators. Then, the generalised estimators, with the optimal shrinkage parameters, are evaluated based on forecasting accuracy. Moreover, the effects of three factors are examined, namely, the length of data history, variance of random components and the number of series. Finally, a simulation experiment is conducted to support the evaluation. Copyright © 2011 John Wiley & Sons, Ltd.