文章基本信息

标题：Kernel Density Estimation and Extended CLT and SLLN in ARCH(p)-Time Series
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作者：Fuxia Cheng ; Illinois State University, Normal, USA
期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2007
卷号：69
期号：04
出版社：Indian Statistical Institute
摘要：In this paper we consider the estimation of the innovation density and the asymptotics of the sum of residuals and the sum of squared residuals in ARCH(p)-time series. We obtain the weak and strong uniform consistency of the kernel density estimators based on the residuals. We extend the Central Limit Theorem (CLT) and the Strong Law of Large Number (SLLN) to the average of residuals. For the average of squared residuals, we show its weak and strong consistency to the innovation variance.
关键词：ARCH(p)-time series, Kernel density estimation, residuals, CLT, SLLN.