Nonparametric prediction of nonstationary spatio-temporal
In spatial statistics often the response variable at a given location
and time is observed together
with some covariates which are known to influence the response.
In several applications the relationship between the response and
covariates may be unknown, and to prevent misspecification of the model,
a nonparametric approach could be appropriate.
In this paper prediction and forecasting of the response variable,
for spatially nonstationary, spatio-temporal processes,
within a nonparametric framework is developed. The linear prediction of the
response, which involves estimation of the covariance structure, and
also the more general
optimal predictor are investigated. The asymptotic sampling properties
of the predictors are studied.
It is shown that in order to avoid the curse of dimensionality
the covariance estimator should be defined in terms of
the dependence structure of the spatio-temporal process.
Furthermore the rate of convergence of the prediction estimators
depend on the temporal dependence of the covariates and the mixing rates
of the spatio-temporal process.
The model defined and the estimation methodology has many possible
applications. We consider a specific application and illustrate our
methodology by modelling house prices in the
Stockport area, United Kingdom, using the deprivation index and district
as the covariates.