Inference on periodograms of infinite dimensional discrete time periodically correlated processes

  • Authors:

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

  • Affiliations:

  • Department of Statistics and Operations Research, Faculty of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait and Department of Statistics, Faculty of Science, Shiraz University, Shi ...;Department of Statistics, Faculty of Science, Shiraz University, Shiraz 71454, Iran;Department of Statistics, Faculty of Science, Shiraz University, Shiraz 71454, Iran

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2010

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Abstract

In this work we shall consider two classes of weakly second-order periodically correlated and strongly second-order periodically correlated processes with values in separable Hilbert spaces. The periodogram for these processes is introduced and its statistical properties are studied. In particular, it is proved that the periodogram is asymptotically unbiased for the spectral density of the processes, where the type of the convergence is fully specified.