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Kalman filtering from POP-based diagonalization of ARH(1) |
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| Authors: | M.D. Ruiz-Medina,R. Salmeró n |
| Affiliation: | a Department of Statistics and Operation Researchs, Faculty of Sciencies, Avda. Fuentenueva, s/n, University of Granada, 18071 Granada, Spain b Department of Quantitative Methods for Economics and Bussiness, Faculty of Economics and Bussiness Sciences, Campus Universitario de Cartuja, s/n, University of Granada, 18011 Granada, Spain |
| Abstract: | The autoregressive Hilbertian model of order one (ARH(1)) is considered to represent the dynamics of a sequence of spatial functional data. Spatiotemporal interaction is defined in terms of the autocorrelation operator. A diagonalization of ARH(1) models is derived based on the functional principal oscillation pattern (POP) decomposition of such an operator. The results are applied to implement the Kalman filter for spatiotemporal prediction from the information provided by the observation of a finite sequence of spatial functional data. |
| Keywords: | Autoregressive Hilbertian model Dimension reduction Optimal decomposition Spatial functional data Spatiotemporal interaction model |
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