混合GM(1,1)模型预报季节性时间序列精度的方法探讨

灰色系统已被成功用于工程、经济、物理控制等许多领域。然而在预报具有季节性的时间序列时，直接应用GM(1，1)灰色模型往往精度不高。因为GM(1，1)灰色模型只能反映时间序列的总体变化趋势，不能很好反映其季节性波动变化的具体特征。因此，作者提出运用“滑动平均去季节性波动”与GM(1，1)混合建模的方法预报具有季节特征的时间序列。并以水文地质系统中地下水位预报和安装在混凝土中的测缝计测得的建筑物形变量为一组时间序列，基于均方差、平均绝对误差和平均绝对百分误差三个精度准则，比较了此方法与其它灰色建模法的结果。结果表明，此方法不仅能反映时间序列的总体变化趋势，而且能客观反映其波动变化的具体特征，有效提高了预报精度，减少了建模的复杂度。

Hybrid GM(1,1) Model to Forecast the Time Series with Seasonality

The grey forecasting model has been successfully applied to such fields as engineering, economics, and physical control, etc. However, the precision of GM(1,1) grey forecast model are not preferable to model the time series with obvious seasonality. It reflects with high accuracy the general trend of the time series while fails to reflect the characteristics of seasonal fluctuation. Therefore, the author proposes a hybrid model that combines the ratio-to-moving-average deseasonalization method and GM(1,1) grey forecasting model to forecast time series with seasonality characteristics . A time series data of the underground water level and a data series of continuous measurement of a joint meter installed in a concrete structure were used as test data sets to compare the performance of the hybrid model against other models, and three evaluation criteria,i.e.MSE, MAE, MAPE, were used to evaluate forecasting models. It proves that the hybrid model can not only reflects the general trend of the time series, but also the characteristics of seasonalfluctuation, and therefore improve the forecasting precision a great deal. Besides, it largely diminishes modeling complexity.