A comparison of neighbourhood selection techniques in spatiotemporal forecasting models

Abstract

Spatio-temporal neighbourhood (STN) selection is an important part of the model building procedure in spatio-temporal forecasting. The STN can be defined as the set of observations at neighbouring locations and times that are relevant for forecasting the future values of a series at a particular location at a particular time. Correct specification of the STN can enable forecasting models to capture spatio-temporal dependence, greatly improving predictive performance. In recent years, deficiencies have been revealed in models with globally fixed STN structures, which arise from the problems of heterogeneity, nonstationarity and nonlinearity in spatio-temporal processes. Using the example of a large dataset of travel times collected on London's road network, this study examines the effect of various STN selection methods drawn from the variable selection literature, varying from simple forward/backward subset selection to simultaneous shrinkage and selection operators. The results indicate that STN selection methods based on L1 penalisation are effective. In particular, the maximum concave penalty (MCP) method selects parsimonious models that produce good forecasting performance.