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The prediction theory of stationary random fields. III. Fourfold Wold decompositions

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  • Chiang, Tse-Pei

Abstract

In this paper, we investigate various fourfold Wold-type decompositions of stationary random fields under different hypotheses of commutation properties. Spectral characterizations of the three multiplicities of the innovation subspaces are obtained. The equivalence relations between the weak commutation property, fourfold Wold-type decomposition, and quarter-plane moving average representation are proved. A complete spectral characterization of the weak commutation property is also given.

Suggested Citation

  • Chiang, Tse-Pei, 1991. "The prediction theory of stationary random fields. III. Fourfold Wold decompositions," Journal of Multivariate Analysis, Elsevier, vol. 37(1), pages 46-65, April.
    • Handle: RePEc:eee:jmvana:v:37:y:1991:i:1:p:46-65
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    Cited by:

    1. Cuny, Christophe, 2006. "On the prediction of vector-valued random fields and the spectral distribution of their evanescent component," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1842-1869, September.
    2. Cheng, Raymond, 2015. "Prediction of stationary Gaussian random fields with incomplete quarterplane past," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 245-258.
    3. Kliger, Mark & Francos, Joseph M., 2010. "The rank of the covariance matrix of an evanescent field," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 692-705, March.
    4. Kliger, Mark & Francos, Joseph M., 2007. "Asymptotic normality of the sample mean and covariances of evanescent fields in noise," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1853-1875, November.

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