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

István Berkes, Lajos Horvath and Gregory Rice

Journal of Multivariate Analysis, 2016, vol. 144, issue C, 150-175

Abstract: We consider the asymptotic normality in L2 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.

Keywords: Functional time series; Long run covariance operator; Normal approximation; Moment inequalities; Empirical eigenvalues and eigenfunctions (search for similar items in EconPapers)
Date: 2016
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Handle: RePEc:eee:jmvana:v:144:y:2016:i:c:p:150-175