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On infinite dimensional periodically correlated random fields: Spectrum and evolutionary spectra

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  • Haghbin, H.
  • Shishebor, Z.

Abstract

Infinite dimensional periodically correlated (PC) random fields are studied in spectral domain. A spectral characterization is given and harmonizability is established. The covariance operator is characterized where it is observed that an infinite dimensional PC field is a two-dimensional Fourier transform of a spectral random measure. Also, an evolutionary spectral representation and a space-dependent spectral density are given.

Suggested Citation

  • Haghbin, H. & Shishebor, Z., 2016. "On infinite dimensional periodically correlated random fields: Spectrum and evolutionary spectra," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 257-267.
    • Handle: RePEc:eee:stapro:v:110:y:2016:i:c:p:257-267
    DOI: 10.1016/j.spl.2015.10.003
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    References listed on IDEAS

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    1. Hurd, H. & Kallianpur, G. & Farshidi, J., 2004. "Correlation and spectral theory for periodically correlated random fields indexed on Z2," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 359-383, August.
    2. H. Haghbin & Z. Shishebor & A. Soltani, 2014. "Hilbertian spatial periodically correlated first order autoregressive models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 303-319, September.
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    1. H. Haghbin & Z. Shishebor & A. Soltani, 2014. "Hilbertian spatial periodically correlated first order autoregressive models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 303-319, September.

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