平稳ARIMA(p,d,q)模型的经验似然推断

J4 ›› 2009, Vol. 47 ›› Issue (05): 871-876.

平稳ARIMA(p,d,q)模型的经验似然推断

张海祥, 王德辉

吉林大学数学学院, 长春 130012

收稿日期:2008-11-20 出版日期:2009-09-26 发布日期:2009-11-03
通讯作者: 王德辉 E-mail:Wangdehui69@163.com.

Empirical Likelihood Inference for the StationaryARIMA(p,d,q) Model

ZHANG Hai-Xiang, WANG De-Hui

College of Mathematics, Jilin University, Changchun 130012, China

Received:2008-11-20 Online:2009-09-26 Published:2009-11-03
Contact: WANG De-Hui E-mail:Wangdehui69@163.com.

摘要/Abstract

摘要：

研究平稳ARIMA(p,d,q)模型的经验似然方法, 利用周
期图纵坐标I(ωj)的极限性质, 给出了参数的估计方程及Whittle’s估计因子, 并证明了
对数截面经验似然比统计量L(β)的极限分布是自由度为p+q+2的χ²分布, 同时给出了模
型参数的置信域.

关键词: ARIMA模型；估计方程；经验似然；周期图；谱密度

Abstract:

he authors studied the empirical likelihood method for
stationary ARIMA(p,d,q) model, which is based on the periodogram ordinate’s
asymptotical property, obtained the estimation equation and whittle’s estimat
or for the model parameter and the distribution of the log profile empiri
cal likelihood ratio statistic L(β) which is asymptotically distributed as
χ²p+q+2, as well as the confidence regions for the parameters.

Key words: ARIMA model, estimation equation, empirical likelihood, periodogram, spectral density

中图分类号:

O212.7

张海祥, 王德辉. 平稳ARIMA(p,d,q)模型的经验似然推断[J]. J4, 2009, 47(05): 871-876.

ZHANG Hai-Xiang, WANG De-Hui. Empirical Likelihood Inference for the StationaryARIMA(p,d,q) Model[J]. J4, 2009, 47(05): 871-876.

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