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On the asymptotic normality of kernel estimators of the long run covariance of functional time series (1503.00741v2)
Published 2 Mar 2015 in math.ST and stat.TH
Abstract: We consider the asymptotic normality in $L2$ of kernel estimators of the long run covariance kernel 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.