Statistical inference for time-varying ARCH processes

• 成果类型: Article
• 署名作者: Dahlhaus, Rainer; Rao, Suhasini Subba
• 署名单位: Ruprecht Karls University Heidelberg
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000227
• 发表日期: 2006
• 页码: 1075-1114
• 关键词: conditional heteroskedasticity; garch processes; models

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.