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Hilbertian spatial periodically correlated first order autoregressive models

Author

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  • H. Haghbin
  • Z. Shishebor
  • A. Soltani

Abstract

In this article, we consider Hilbertian spatial periodically correlated autoregressive models. Such a spatial model assumes periodicity in its autocorrelation function. Plausibly, it explains spatial functional data resulted from phenomena with periodic structures, as geological, atmospheric, meteorological and oceanographic data. Our studies on these models include model building, existence, time domain moving average representation, least square parameter estimation and prediction based on the autoregressive structured past data. We also fit a model of this type to a real data of invisible infrared satellite images. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:advdac:v:8:y:2014:i:3:p:303-319
    DOI: 10.1007/s11634-014-0172-8
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    References listed on IDEAS

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    1. Shishebor, Z. & Soltani, A.R. & Zamani, A., 2011. "Asymptotic distribution for periodograms of infinite dimensional discrete time periodically correlated processes," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1118-1125, August.
    2. 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.
    3. A. Soltani & M. Hashemi, 2011. "Periodically correlated autoregressive Hilbertian processes," Statistical Inference for Stochastic Processes, Springer, vol. 14(2), pages 177-188, May.
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    Cited by:

    1. 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.

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