Kernel averaged predictors for spatio-temporal regression models

In regression settings where covariates and responses are observed across space and time, a common goal is to quantify the effect of change in the covariates on the response while adequately accounting for the joint spatio-temporal structure in both. Customary modeling describes the relationship between a covariate and a response variable at a single spatio-temporal location. However, often it is anticipated that the relationship between the response and predictors may extend across space and time. In other words, the response at a given location and time may be affected by levels of predictors in spatio-temporal proximity. Here, a flexible modeling framework is proposed to capture such spatial and temporal lagged effects between a predictor and a response. Specifically, kernel functions are used to weight a spatio-temporal covariate surface in a regression model for the response. The kernels are assumed to be parametric and non-stationary with the data informing the parameter values of the kernel. The methodology is illustrated on simulated data as well as a physical data set of ozone concentrations to be explained by temperature.