  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.
