On the asymptotic normality of kernel estimators of the long run covariance of functional time series

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• 作者：Istvá ; n Berkes^a ; ^b ; Lajos Horvá ; th^c ; Gregory Rice^d ; ^{grice@uwaterloo.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 62E20 ; secondary ; 62F12 ; 62M10
• 刊名：Journal of Multivariate Analysis
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：144
• 期：Complete
• 页码：150-175
• 全文大小：502 K

文摘

We consider the asymptotic normality in L²$L^2$ of kernel estimators of the long run covariance of stationary functional time series. Our results are established assuming a weakly dependent Bernoulli shift structure for the underlying observations, which contains most stationary functional time series models, under mild conditions. As a corollary, we obtain joint asymptotics for functional principal components computed from empirical long run covariance operators, showing that they have the favorable property of being asymptotically independent.