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Asymptotic distribution for periodograms of infinite dimensional discrete time periodically correlated processes

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  • Shishebor, Z.
  • Soltani, A.R.
  • Zamani, A.

Abstract

In this article we shall consider a class of strongly T-periodically correlated processes with values in a separable complex Hilbert space . The periodograms of these processes and their statistical properties were previously studied by the authors. In this paper we derive the asymptotic distribution of the periodogram, that appears to be a certain Wishart distribution on .

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:7:p:1118-1125
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    References listed on IDEAS

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    1. Kundu, Subrata & Majumdar, Suman & Mukherjee, Kanchan, 2000. "Central Limit Theorems revisited," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 265-275, April.
    2. Soltani, A.R. & Shishebor, Z. & Zamani, A., 2010. "Inference on periodograms of infinite dimensional discrete time periodically correlated processes," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 368-373, February.
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    Cited by:

    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.
    2. A. R. Soltani & A. R. Nematollahi & M. R. Mahmoudi, 2019. "On the asymptotic distribution of the periodograms for the discrete time harmonizable simple processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(2), pages 307-322, July.
    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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