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Spatial autoregressive and moving average Hilbertian processes


  • Ruiz-Medina, M.D.


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.

Suggested Citation

  • Ruiz-Medina, M.D., 2011. "Spatial autoregressive and moving average Hilbertian processes," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 292-305, February.
  • Handle: RePEc:eee:jmvana:v:102:y:2011:i:2:p:292-305

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    References listed on IDEAS

    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.
    4. Yao, Qiwei & Brockwell, Peter J, 2006. "Gaussian maximum likelihood estimation for ARMA models II: spatial processes," LSE Research Online Documents on Economics 5416, London School of Economics and Political Science, LSE Library.
    5. repec:taf:gnstxx:v:22:y:2010:i:4:p:477-497 is not listed on IDEAS
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    Cited by:

    1. repec:spr:joptap:v:167:y:2015:i:3:d:10.1007_s10957-013-0423-4 is not listed on IDEAS
    2. Maria Ruiz-Medina & Rosa Espejo & Elvira Romano, 2014. "Spatial functional normal mixed effect approach for curve classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 257-285, September.
    3. Álvarez-Liébana, J. & Bosq, D. & Ruiz-Medina, M.D., 2017. "Asymptotic properties of a component-wise ARH(1) plug-in predictor," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 12-34.


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