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Characterization of the Spectra of Periodically Correlated Processes

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  • Makagon, Andrzej

Abstract

A complete characterization of the spectrum of a locally square integrable periodically correlated (PC) processes is obtained. The result makes use of the author's recent theorem establishing a one to one correspondence between PC processes and a certain class on infinite dimensional stationary processes. In terms of distributions it is proved that the Fourier transform of a positive definite distribution on the plane which is the sum of complex uniformly bounded measures supported on equidistant lines parallel to diagonal is a locally square integrable function.

Suggested Citation

  • Makagon, Andrzej, 2001. "Characterization of the Spectra of Periodically Correlated Processes," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 1-10, July.
    • Handle: RePEc:eee:jmvana:v:78:y:2001:i:1:p:1-10
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    References listed on IDEAS

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    1. Makagon, A. & Miamee, A. G. & Salehi, H., 1994. "Continuous time periodically correlated processes: Spectrum and prediction," Stochastic Processes and their Applications, Elsevier, vol. 49(2), pages 277-295, February.
    2. Hurd, H. L., 1989. "Representation of strongly harmonizable periodically correlated processes and their covariances," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 53-67, April.
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