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Spatial autoregressive and moving average Hilbertian processes

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  • Ruiz-Medina, M.D.
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    Abstract

    This paper addresses the introduction and study of structural properties of Hilbert-valued spatial autoregressive processes (SARH(1) processes), and Hilbert-valued spatial moving average processes (SMAH(1) processes), with innovations given by two-parameter (spatial) matingale differences. For inference purposes, the conditions under which the tensorial product of standard autoregressive Hilbertian (ARH(1)) processes (respectively, of standard moving average Hilbertian (MAH(1)) processes) is a standard SARH(1) process (respectively, it is a standard SMAH(1) process) are studied. Examples related to the spatial functional observation of two-parameter Markov and diffusion processes are provided. Some open research lines are described in relation to the formulation of SARMAH processes, as well as General Spatial Linear Processes in Functional Spaces.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 102 (2011)
    Issue (Month): 2 (February)
    Pages: 292-305

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    Handle: RePEc:eee:jmvana:v:102:y:2011:i:2:p:292-305

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    Related research

    Keywords: Spatial functional statistics Spatial Hilbert-valued processes Tensorial product of Hilbert-valued processes Two-parameter Markov processes Two-parameter martingale differences;

    References

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    1. Nerini, David & Monestiez, Pascal & Manté, Claude, 2010. "Cokriging for spatial functional data," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 409-418, February.
    2. Bosq, Denis, 2010. "Tensorial products of functional ARMA processes," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1352-1363, July.
    3. Ruiz-Medina, M.D. & Salmeron, R. & Angulo, J.M., 2007. "Kalman filtering from POP-based diagonalization of ARH(1)," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4994-5008, June.
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