Modeling Spatial-Temporal Data with a Short Observation History

Abstract

A novel method is proposed for forecasting spatial-temporal data with a short observation history sampled on a uniform grid. The method is based on spatial-temporal autoregressive modeling where the predictions of the response at the subsequent temporal layer are obtained using the response values from a recent history in a spatial neighborhood of each sampling point. Several modeling aspects such as covariance structure and sampling, as well as identification, model estimation and forecasting issues, are discussed. Extensive experimental evaluation is performed on synthetic and real-life data. The proposed forecasting models were shown capable of providing a near optimal prediction accuracy on simulated stationary spatial-temporal data in the presence of additive noise and a correlated model error. Results on a spatial-temporal agricultural dataset indicate that the proposed methods can provide useful prediction on complex real-life data with a short observation history.