Applied hybrid grey model to forecast - Seasonal time series

The grey forecasting model has been successfully applied to finance, physic al control, engineering, economics, etc. However, no seasonal time series f orecast has been tested. The authors of this paper proved that GM(1,1) grey forecasting model is insufficient for forecasting time series with seasona lity. This paper proposes a hybrid method that combines the GM(1,1) grey fo recasting model and the ratio-to-moving-average deseasonalization method to forecast time series with seasonality characteristics. Three criteria, i.e ., the mean squares error (MSE), the mean absolute error (MAE), and mean ab solute percentage error (MAPE) were used to compare the performance of the hybrid model against other four models, i.e., the seasonal time series ARIM A model (SARIMA), the neural network back-propagation model combined with g rey relation, the GM(1,1) grey model with raw data, the GM(1,N) grey model combined with grey relation. The time series data of the total production v alue of Taiwan's machinery industry (January 1994 to December 1997) and the sales volume of soft drink reported from Montgomery's book were used as te st data sets. Except for the out-of-sample error of the Taiwan machinery pr oduction value time series, the MSE, the MAE, and the MAPE of the hybrid mo del were the lowest. (C) 2001 Elsevier Science Inc.