基于小波分析的ARMA-GARCH模型在降水预报中的应用  

Application of ARMA-GARCH Model Based on Wavelet Analysis in Rainfall Forecasting

作　　者：王喜华[1] 卢文喜[1] 初海波[1] 陈社明[1] 

机构地区：[1]吉林大学环境与资源学院,长春130026

出　　处：《节水灌溉》2011年第5期52-56,共5页Water Saving Irrigation

基　　金：吉林省科技发展计划项目"吉林省水稻节水灌溉与水分管理的技术与模式研究"(20100215)

摘　　要：利用小波分析方法对通榆地区1955-1999年降水资料进行分解与单支重构,得到低频序列和高频序列;对得到的子序列依据是否具有自回归条件异方差（ARCH）效应,建立自回归移动平均（ARMA）模型或者ARMA-GARCH模型。然后将上述各子序列所建模型进行线性叠加,得到年降水量的基于小波分析的ARMA-GARCH模型（W-A-G）。根据2000-2009年的降水资料检验模型,并与未考虑ARCH效应的基于小波分析的ARMA模型（W-A）作对比。结果表明：小波分析的6个子序列中,低频项（A5）不具有ARCH效应,高频项（D1~D5）具有明显ARCH效应;W-A-G模型检验的相对误差平均值为9.98%,平均绝对百分比误差（MAPE）值为0.009 9,根均方差（RMSE）值为34.592 8,符合水文预测标准且精度明显高于W-A模型（平均相对误差22.4%,MAPE为0.180 2,RMSE为83.337 3）,表明W-A-G模型是一种可行的方法。最后用所建W-A-G模型对通榆地区未来6年降水量进行预测,预测结果显示：通榆地区未来降水量呈下降趋势,干旱情况将持续发生,应做好抗旱准备。The low-frequency sequence and high-frequency sequences of Tongyu areas precipitation data from 1955 to 1999 are got by using single signal decomposition and reconstruction with wavelet methods.According to whether the sequence have the auto regressive conditional heteroskedasticity（ARCH） effects or not,the custom regressive moving average（ARMA） model or ARMA-GARCH model is created.Then,the final annual precipitation ARMA-GARCH model（W-A-G） based on wavelet analysis is gained through a linear superposition of the model which have been established by the above sequences.The 2000-2009 precipitation data is used to test the model and compared with the ARMA model based on wavelet analysis（W-A） which is not considered the ARCH effect.The results showed that among the 6 sub-sequence of wavelet decomposition,the low-frequency items（A5） does not have the ARCH effect,high-frequency items（D1~D5） have significant ARCH effect;the average relative error of W-A-G model checking is 9.98%,the average absolute percentage error（MAPE） is 0.009 9,the root mean square error（RMSE） value is 34.5928,which is accorded with the hydrological forecasting standard and has higher accurate than the W-A model,in which the average relative error is 22.4%,MAPE is 0.180 2,RMSE is 83.337 3.This shows that the W-A-G model is a feasible method.Finally,the WAG model is used to forecast the precipitation in the next 6 years of Tongyu area.The predicted results show that precipitation of Tongyu region will decrease in the future and drought conditions will continually occur.The anti-drought measures should be prepared.

关 键 词：ARMA-GARCH模型 小波分析 降水预报 通榆地区 

分 类 号：TV125[水利工程—水文学及水资源]