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Asymptotic distribution for periodograms of infinite dimensional discrete time periodically correlated processes. (English) Zbl 1244.60038
From the abstract: “In this article, we shall consider a class of strongly \(T\)-periodically correlated processes with values in a separable complex Hilbert space H. 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 H\(^T\).”

MSC:
60G12 General second-order stochastic processes
60G57 Random measures
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
60F05 Central limit and other weak theorems
62M15 Inference from stochastic processes and spectral analysis
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