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Inference on periodograms of infinite dimensional discrete time periodically correlated processes. (English) Zbl 1178.62106
Summary: We consider two classes of weakly second-order periodically correlated and strongly second-order periodically correlated processes with values in separable Hilbert spaces. The periodogram for these processes is introduced and its statistical properties are studied. In particular, it is proved that the periodogram is asymptotically unbiased for the spectral density of the processes, where the type of the convergence is fully specified.

MSC:
62M15 Inference from stochastic processes and spectral analysis
46N30 Applications of functional analysis in probability theory and statistics
60G12 General second-order stochastic processes
60G57 Random measures
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