Statistical inference for time-varying ARCH processes

被引：118

作者：

Dahlhaus, Rainer ^{[1
]}

Rao, Suhasini Subba ^{[1
]}

机构：

[1] Univ Heidelberg, Inst Angewandte Math, D-69120 Heidelberg, Germany

来源：

ANNALS OF STATISTICS | 2006年 / 34卷 / 03期

关键词：

derivative process; locally stationary; quasi-likelihood estimates; timevarying; ARCH process;

D O I：

10.1214/009053606000000227

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper the class of ARCH(infinity) models is generalized to the nonstationary class of ARCH(infinity) models with time-varying coefficients. For fixed time points, a stationary approximation is given leading to the notation "locally stationary ARCH(infinity) process." The asymptotic properties of weighted quasi-likelihood estimators of time-varying ARCH(p) processes (p < infinity) are studied, including asymptotic normality. In particular, the extra bias due to nonstationarity of the process is investigated. Moreover, a Taylor expansion of the nonstationary ARCH process in terms of stationary processes is given and it is proved that the time-varying ARCH process can be written as a time-varying Volterra series.

引用

页码：1075 / 1114

页数：40

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