Spatial autoregressive and moving average Hilbertian processes

M.D. Ruiz-Medina

Journal of Multivariate Analysis, 2011, vol. 102, issue 2, 292-305

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.

Keywords: Spatial; functional; statistics; Spatial; Hilbert-valued; processes; Tensorial; product; of; Hilbert-valued; processes; Two-parameter; Markov; processes; Two-parameter; martingale; differences (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (6)

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