How much time to include in multiscale space-time regressions? Optimising predictor variable temporal lags

Abstract. Generalised Additive Models (GAMs) with Gaussian process bases have been proposed as a framework for constructing spatially varying coefficient (SVC) and spatially and temporally varying coefficient (STVC) regression models, that overcome many of the theoretical problems and technical limitations associated with geographically weighted approaches. Recent work has considered the SVC case in detail and this is being extended to the temporal case. However, while spatial lags and dependencies are well handled by many existing methods, one of the critical issues in space-time modelling is how to determine appropriate temporal lags for individual predictor variables that may exhibit different temporal dependencies with the target variable. This paper demonstrates an outline approach for optimising these. Additionally, lags determined in this way may be used to inform on the temporal margins used to parameterise space-time tensor products smooths in GAM based STVC approaches.