Asymptotic distribution for periodograms of infinite dimensional discrete time periodically correlated processes

In this article we shall consider a class of strongly T-periodically correlated processes with values in a separable complex Hilbert space . The periodograms of these processes and their statistical properties were previously studied by the authors. In this paper we derive the asymptotic distribution of the periodogram, that appears to be a certain Wishart distribution on .Hilbert space-valued processes Strong second order processes Periodically correlated Finite Fourier transforms Periodogram Asymptotic distribution