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Spectral factorization of wide sense stationary processes on 2

Author

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  • Korezlioglu, Hayri
  • Loubaton, Philippe

Abstract

The problem of prediction of wide sense stationary processes on 2 with respect to the column-by-column or row-by-row lexicographic order is studied. A theorem giving an explicit realization of the corresponding canonical factorization of the spectral density is proved and conditions are given for a process to have a quarter-plane representation in terms of its innovations.

Suggested Citation

  • Korezlioglu, Hayri & Loubaton, Philippe, 1986. "Spectral factorization of wide sense stationary processes on 2," Journal of Multivariate Analysis, Elsevier, vol. 19(1), pages 24-47, June.
    • Handle: RePEc:eee:jmvana:v:19:y:1986:i:1:p:24-47
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    Citations

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    Cited by:

    1. Pham, Viet Son, 2020. "Lévy-driven causal CARMA random fields," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7547-7574.
    2. Gupta, Abhimanyu, 2018. "Autoregressive spatial spectral estimates," Journal of Econometrics, Elsevier, vol. 203(1), pages 80-95.
    3. 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.
    4. Cheng, Raymond, 2015. "Prediction of stationary Gaussian random fields with incomplete quarterplane past," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 245-258.
    5. Abhimanyu Gupta & Javier Hidalgo, 2020. "Nonparametric prediction with spatial data," Papers 2008.04269, arXiv.org, revised Nov 2021.
    6. Abdelouahab Bibi & Karima Kimouche, 2014. "On stationarity and second-order properties of bilinear random fields," Statistical Inference for Stochastic Processes, Springer, vol. 17(3), pages 221-244, October.
    7. Peter Robinson & J. Vidal Sanz Vidal Sanz, 2003. "Modified whittle estimation of multilateral spatial models," CeMMAP working papers 18/03, Institute for Fiscal Studies.
    8. repec:esx:essedp:767 is not listed on IDEAS
    9. Gupta, A, 2015. "Autoregressive Spatial Spectral Estimates," Economics Discussion Papers 14458, University of Essex, Department of Economics.
    10. Peter Robinson & J. Vidal Sanz Vidal Sanz, 2003. "Modified whittle estimation of multilateral spatial models," CeMMAP working papers CWP18/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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