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.

在跨空间和时间观察协变量和响应的回归设置中，一个共同目标是量化协变量变化对响应的影响，同时充分考虑两者的联合时空结构。习惯建模描述了单个时空位置的协变量和响应变量之间的关系。然而，通常预计响应和预测变量之间的关系可能会跨越空间和时间。换句话说，给定位置和时间的响应可能会受到时空接近度的预测因子水平的影响。在这里，提出了一个灵活的建模框架来捕获预测变量和响应之间的这种空间和时间滞后效应。具体来说，核函数用于在响应的回归模型中对时空协变量表面进行加权。内核被假定为参数的和非平稳的，数据通知内核的参数值。该方法在模拟数据以及由温度解释的臭氧浓度物理数据集上进行了说明。