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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:144

Article

Berkes, Istvan^1,2  Horvath, Lajos³  Rice, Gregory⁴ 

[1] Graz Univ Technol, Inst Stat, A-8010 Graz, Austria

[2] Hungarian Acad Sci, Math Inst, Budapest, Hungary

[3] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

[4] Univ Waterloo, Dept Stat & Actuarial Sci, Waterloo, ON N2L 3G1, Canada

关键词: Functional time series;    Long run covariance operator;    Normal approximation;    Moment inequalities;    Empirical eigenvalues and eigenfunctions;   

DOI  :  10.1016/j.jmva.2015.11.005

来源: Elsevier

【 摘 要 】

We consider the asymptotic normality in 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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free