Convergence Rate of Empirical Autocovariance Operators in H-Valued Periodically Correlated Processes

Abstract

. This paper focuses on the empirical autocovariance operator of H -valued periodically correlated processes. It will be demonstrated that the empirical estimator converges to a limit with the same periodicity as the main process. Moreover, the rate of convergence of the empirical autocovariance operator in Hilbert-Schmidt norm is derived.