Inference on periodograms of infinite dimensional discrete time periodically correlated processes

In this work we shall 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,...

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Bibliographic Details
Published in:Journal of multivariate analysis 2010-02, Vol.101 (2), p.368-373
Main Authors: Soltani, A.R., Shishebor, Z., Zamani, A.
Format: Article
Language:English
Subjects:
60G12
60G57
60G57 Hilbert space-valued second-order processes Periodically correlated processes Finite Fourier transforms Periodogram
Asymptotic methods
Correlation analysis
Euclidean space
Exact sciences and technology
Finite Fourier transforms
Functional analysis
Hilbert space-valued second-order processes
Mathematical analysis
Mathematics
Multivariate analysis
Periodically correlated processes
Periodogram
primary
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistical inference
Statistics
Stochastic processes
Studies
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Summary:In this work we shall 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.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2009.01.004