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Inference on periodograms of infinite dimensional discrete time periodically correlated processes

Author

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

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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:2:p:368-373
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    References listed on IDEAS

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    1. Rozanov, Yu. A., 1972. "Some approximation problems in the theory of stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 2(2), pages 135-144, June.
    2. Chen, Xiaohong & White, Halbert, 1998. "Central Limit And Functional Central Limit Theorems For Hilbert-Valued Dependent Heterogeneous Arrays With Applications," Econometric Theory, Cambridge University Press, vol. 14(2), pages 260-284, April.
    3. Hurd, H. L., 1989. "Representation of strongly harmonizable periodically correlated processes and their covariances," Journal of Multivariate Analysis, Elsevier, vol. 29(1), pages 53-67, April.
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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.

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