Long memory conditional random fields on regular lattices

摘要

This paper draws its motivation from applications in geophysics, agricultural,and environmental sciences where empirical evidence of slow decay of correlationshave been found for data observed on a regular lattice. Spatial ARFIMAmodels represent a widely used class of spatial models for analyzing such data.Here, we consider their generalization to conditional autoregressive fractionalintegrated moving average (CARFIMA) models, a larger class of long memorymodels which allows a wider range of correlation behavior. For this class weprovide detailed descriptions of important representative models,make the necessarycomparison with some other existing models, and discuss some importantinferential and computational issues on estimation, simulation and longmemory process approximation. Results from model fit comparison and predictiveperformance of CARFIMA models are also discussed through a statisticalanalysis of satellite land surface temperature data.