On the asymptotic normality of kernel estimators of the long run covariance of functional time series
Lajos Horvath and
Journal of Multivariate Analysis, 2016, vol. 144, issue C, 150-175
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)
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