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

  • Authors:

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

  • Affiliations:

  • Department of Statistics, Faculty of Science, Shiraz University, Shiraz 71454, Iran;Department of Statistics, Faculty of Science, Shiraz University, Shiraz 71454, Iran and Department of Statistics and Operations Research, Faculty of Science, Kuwait University, P.O. Box 5969, Safa ...;Department of Statistics, Faculty of Science, Shiraz University, Shiraz 71454, Iran

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2011

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Abstract

In this article we shall consider a class of strongly T-periodically correlated processes with values in a separable complex Hilbert space H. 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 H^T.