Applied Hybrid Grey Model to Forecast Seasonal Time Series

Abstract

The grey forecasting model has been successfully applied to finance, physical control, engineering, economics, etc. However, no seasonal time series forecast has been tested. The authors of this paper proved that GM(1,1) grey forecasting model is insufficient for forecasting time series with seasonality. This paper proposes a hybrid method that combines the GM(1,1) grey forecasting 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 absolute percentage error (MAPE) were used to compare the performance of the hybrid model against other four models, i.e., the seasonal time series ARIMA model (SARIMA), the neural network back-propagation model combined with grey 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 value 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 test data sets. Except for the out-of-sample error of the Taiwan machinery production value time series, the MSE, the MAE, and the MAPE of the hybrid model were the lowest.