Statistical inference for the logarithmic spatial heteroskedasticity model with exogenous variables

TL;DR

This paper introduces a new spatial heteroscedasticity model that captures dependence in variance, along with comprehensive statistical inference procedures, validated through simulations and real estate data analysis.

Contribution

It proposes the log-SHE model for spatial variance dependence and develops inference methods with asymptotic properties, filling a gap in spatial heteroskedasticity modeling.

Findings

The log-SHE model effectively captures spatial variance dependence.

Proposed estimators and tests have established asymptotic properties.

Simulation and real data demonstrate the model's practical utility.

Abstract

The spatial dependence in mean has been well studied by plenty of models in a large strand of literature, however, the investigation of spatial dependence in variance is lagging significantly behind. The existing models for the spatial dependence in variance are scarce, with neither probabilistic structure nor statistical inference procedure being explored. To circumvent this deficiency, this paper proposes a new generalized logarithmic spatial heteroscedasticity model with exogenous variables (denoted by the log-SHE model) to study the spatial dependence in variance. For the log-SHE model, its spatial near-epoch dependence (NED) property is investigated, and a systematic statistical inference procedure is provided, including the maximum likelihood and generalized method of moments estimators, the Wald, Lagrange multiplier and likelihood-ratio-type D tests for model parameter constraints, and the overidentification test for the model diagnostic checking. Using the tool of spatial NED, the asymptotics of all proposed estimators and tests are established under regular conditions. The usefulness of the proposed methodology is illustrated by simulation results and a real data example on the house selling price.