广义加性模型配合时间序列资料时消除残差自相关性的一种方法  

A Method for Removing Residual Autocorrelation of Time Series in Generalized Additive Models

作　　者：余松林[1] 彭晓武[2] 

机构地区：[1]华中科技大学同济医学院公共卫生学院,430030 [2]环境保护部华南环境科学研究所,510655

出　　处：《中国卫生统计》2010年第5期450-454,共5页Chinese Journal of Health Statistics

基　　金：2007年国家环保公益性行业科研专项项目(NO:200709004)

摘　　要：目的广义加性模型假定观察是独立的,但时间序列资料往往存在自相关性。本文探讨在使用广义加性模型配合时间序列资料时消除残差自相关性的一种方法。方法在广义加性模型基础上加入反应变量函数的非参数匀滑函数项。结果本文实例中采用反应变量的滞后项作为反应变量的函数,使1-12阶的残差自相关系数由加入反应变量函数的非参数匀滑函数项之前的0.50～0.25下降为0.09～-0.09,取得了较满意的效果。结论在用广义加性模型配合时间序列资料时,加入反应变量函数的非参数匀滑函数项可以有效控制自相关带给参数假设检验的影响。Objective The generalized additive models are assumed that observations are independent.Generally,there is autocorrelation among time series data.The paper explores a method for removing residual autocorrelation in fitting time series data with generalized additive models.Methods Based on the structure of generalized additive models,spline function（s）of lagged response variable is added to the models in order to remove autocorrelation existing in residuals.Results An working example is used to illustrate the method.In the example different lagged response variable as spline functions enterred into the model for removing autocorrelation among residuals.The 1 to 12 order autocorrelations of residuals declined from 0.50 to 0.25 before to 0.09 to-0.09 after adding spline functions of different lagged response variable.The effect of removing autocorrelation of residuals is significant.Conclusion In using generalized additive models to fit time series data,inclusion of spline functions of different lagged response variable can remove residual autocorrenaltion effectively,and can reduce the error significantly in hypothesis testing.

关 键 词：时间序列 泊松分布 广义线性模型 广义加性模型 残差自相关性 

分 类 号：R195[医药卫生—卫生统计学]