Predictive Spatio-temporal Models for Spatially Sparse Environmental Data

• Activity Number: 158
• Type: Invited
• Date/Time: Monday, August 4, 2003 : 2:00 PM to 3:50 PM
• Sponsor: ASA-SRCOS So. Regional Cmte on Stats Summer Research
• Author(s): Marc G. Genton*+ and Xavier De Luna
• Companies: North Carolina State University and Umea University
• Keywords: accumulated prediction errors ; spatio-temporal correlation ; vector autoregression ; partial correlation ; ozone data ; wind speed data

Abstract

We present a family of spatio-temporal models which are geared to provide time-forward predictions based on data collected at few spatial locations, but at many regular time intervals. When predictions in the time direction is the purpose of the analysis, then spatial-stationarity assumptions which are commonly used in spatial modeling, are not necessary. The family of models proposed does not make such assumptions and consists in a VAR (vector autoregressive) specification, where there are as many time series as stations. By taking into account the spatial dependence structure, a model building strategy is proposed. As for time series AR models, model building may be performed either by displaying sample partial correlation functions, or by minimizing an information criterion. Two spatio-temporal datasets are used to illustrate the usefulness of the models. In particular, we find evidence that a parametric modeling of the spatio-temporal correlation function is not appropriate because it rests on too strong assumptions. We compare model selection strategies with an out-of-sample validation method based on recursive prediction errors.