A Note on Spatial-Temporal Lattice Modeling and Maximum Likelihood Estimation

TL;DR

This paper investigates the asymptotic behavior of maximum likelihood estimates in spatial-temporal lattice models, establishing conditions for their consistency and normality, supported by simulation results.

Contribution

It introduces mild regularity conditions for spatial-temporal weight matrices and derives the asymptotic properties of MLEs in general spatial-temporal linear models.

Findings

MLEs are consistent under specified conditions

MLEs are asymptotically normal

Simulation confirms finite-sample effectiveness

Abstract

Spatial-temporal linear model and the corresponding likelihood-based statistical inference are important tools for the analysis of spatial-temporal lattice data. In this paper, we study the asymptotic properties of maximum likelihood estimates under a general asymptotic framework for spatial-temporal linear models. We propose mild regularity conditions on the spatial-temporal weight matrices and derive the asymptotic properties (consistency and asymptotic normality) of maximum likelihood estimates. A simulation study is conducted to examine the finite-sample properties of the maximum likelihood estimates.