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Maximum of entropy and extension of covariance matrices for periodically correlated and multivariate processes

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  • Castro, Glaysar
  • Girardin, Valerie

Abstract

A one-to-one relationship exists between scalar periodically correlated nonstationary processes and multivariate stationary processes. This fact allows us to transfer results proven for ones to the others. We are interested in a probabilistic approach of results sometimes already known in a different (analytical or numerical) context, in order to simplify, generalize and unify them. We use a probabilistic approach of generalized reflection coefficients to give a constructive condition of extension of partial covariance sequences, achieved by an autoregressive model. We develop a Trench-Zohar recursion for the nonstationary case which leads to an economical algorithm to solve the associated Yule-Walker equations. Shannon and Burg entropies are linked through a Szëgo type theorem. A numerical example is given.

Suggested Citation

  • Castro, Glaysar & Girardin, Valerie, 2002. "Maximum of entropy and extension of covariance matrices for periodically correlated and multivariate processes," Statistics & Probability Letters, Elsevier, vol. 59(1), pages 37-52, August.
    • Handle: RePEc:eee:stapro:v:59:y:2002:i:1:p:37-52
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    References listed on IDEAS

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    1. Parzen, Emanuel & Pagano, Marcello, 1979. "An approach to modeling seasonally stationary time series," Journal of Econometrics, Elsevier, vol. 9(1-2), pages 137-153, January.
    2. Choi, B. S., 1993. "Multivariate Maximum Entropy Spectrum," Journal of Multivariate Analysis, Elsevier, vol. 46(1), pages 56-60, July.
    3. Degerine, S., 1994. "Sample Partial Autocorrelation Function of a Multivariate Time Series," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 294-313, August.
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    Cited by:

    1. Castro, Glaysar & Girardin, Valerie, 2008. "Characterization of periodically correlated and multivariate stationary discrete time wide Markov processes," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 158-164, February.
    2. Boshnakov, Georgi N. & Lambert-Lacroix, Sophie, 2012. "A periodic Levinson-Durbin algorithm for entropy maximization," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 15-24, January.

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