Adaptive Point SAR Models for Forecasting Random Surfaces

Local spatial autoregressive models with trend (SART) can estimate space-varying parameters and forecast nonstationary random surfaces.

Point spatial data, generated by local measurements of continuous phenomena, are present in numerous physical and social applications. These data are characterized by serial dependece and are modeled with SART (Spatial AutoRegressive plus Trend) models, in which each observation is correlated with its nearest neighbors and spatial coordinates. The primary purpose of these systems is spatial prediction of the dependent variable (i.e., building diffusion maps on regular grids). Real-world data are affected by anisotropy, including trends, heteroskedasticity, and variability of model coefficients; the latter requires adaptive estimation strategies. This project develops local SAR models with bivariate trends (in latitude and longitude), unilateral and multilateral contiguity structures, and weights inversely proportional to the distance, estimated with least squares and maximum likelihood (with the Spatial Econometric Toolbox). Their goal is adaptive spatial prediction, capable of estimating the random components of complex surfaces and showing the spatial variability of regression parameters. This approach represents an alternative to traditional nonparametric smoothing methods, which only detect trend components. An extended interactive file (demo_peak.m) illustrates the approach in detail.