HEWITT, HOETING, DONE, AND TOWLER Figure 1: Schematic illustration of a teleconnection problem. Colorado precipitation Y ( s , t ) is influenced by both local covariates x ( s , t ) and remote covariates z ( r , t ). The remote covariates shown here are standardized anomalies of average monthly Pacific Ocean sea surface temperatures during Winter, 1982. The data come from the ERA-Interim reanalysis dataset (Dee et al., 2011). The RESP model extends the integral in (2) to the entire remote domain D$_{Z}$ and allows θ ( s ) to vary with respect to r , distinguishing it from spatially varying coefficient models (Section 2.1). Integration is a natural construct for aggregating effects of spatially continuous covariates, represents the conceptual limit of studying teleconnection with increasingly fine subsets of R , and allows study of teleconnection with additional spatial structure and without defining indices a priori. The remote effects spatial process (RESP) model extends the standard geostatistical setting in which a local response variable Y ( s , t ) ∈$_{R}$ and known covariate vector x ( s , t ) ∈$_{R}$ p are observable at discrete time points t ∈ T = { t$_{1}$, . . . , t$_{n}$$_{t}$ } and at locations s in a continuous domain D$_{Y}$ . The RESP model includes the effects of known remote covariates z ( r , t ) ∈$_{R}$ , which are observable at locations r in a continuous domain that is spatially disjoint from 2.1 Model formulation 6