Article
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Forecasting Lattice and Point Spatial Data: Comparison of Unilateral and Multilateral Sar Models
Version 1
: Received: 12 August 2024 / Approved: 13 August 2024 / Online: 13 August 2024 (13:03:13 CEST)
How to cite: Grillenzoni, C. Forecasting Lattice and Point Spatial Data: Comparison of Unilateral and Multilateral Sar Models. Preprints 2024, 2024080947. https://doi.org/10.20944/preprints202408.0947.v1 Grillenzoni, C. Forecasting Lattice and Point Spatial Data: Comparison of Unilateral and Multilateral Sar Models. Preprints 2024, 2024080947. https://doi.org/10.20944/preprints202408.0947.v1
Abstract
Spatial auto-regressive (SAR) models are widely used in geosciences for spatial analyses; their main feature is the presence of weight (W) matrices, which define the neighboring relationships between the spatial units. The statistical properties of parameter and forecast estimates strongly depend on the structure of such matrices. The least squares (LS) method is the most flexible and can estimate systems of large dimensions; however, it is not consistent in the presence of multilateral (sparse) matrices. Instead, the unilateral specification of SAR models provides triangular weight matrices which allow good statistical properties to LS and enable the implementation of sequential prediction functions. In this paper we show the better performance in out-of-sample forecasting of unilateral SAR and LS with respect to multilateral and maximum likelihood (ML) methods. This conclusion is supported by extensive numerical simulations and applications to real geological data, both on regular lattice and irregular polygonal form.
Keywords
Contiguity matrices; Consistent estimation; Spatial autoregression; Spatial data; Spatial forecasting.
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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