Spatial long memory

Abstract

We discuss developments and future prospects for statistical modeling and inference for spatial data that have long memory. While a number of contributons have been made, the literature is relatively small and scattered, compared to the literatures on long memory time series on the one hand, and spatial data with short memory on the other. Thus, over several topics, our discussions frequently begin by surveying relevant work in these areas that might be extended in a long memory spatial setting.

Long memory conditional random fields on regular lattices

“…Several papers on spatial LM have appeared in the last decade. However, as highlighted by Robinson (2020), the topic has not been developed as systematically or comprehensively as LM time series and, to the best of our knowledge, there are no comprehensive surveys available in the spatial framework. Some distinctive issues arising in the standard spatial statistics, as for example those regarding inference on second-order properties of stationary random fields, have been studied far more under short memory than LM.…”