REMOTE EFFECTS SPATIAL PROCESS MODELS More generally, the RESP model represents a less-common class of spatial analysis prob- lems that provide rich opportunities for study. We introduce our teleconnection model in the general context of a spatial regression problem involving local and spatially remote co- variates (Section 2.1). The local and spatially remote covariates are allowed to have different spatial correlations structures reflecting their different relationships with the response. Fig- ure 1 schematically illustrates the general teleconnection problem in which local x ( s , t ) and remote z ( r , t ) covariates impact a local spatio-temporal response Y ( s , t ). The RESP model accounts for the influence of covariates observed on a geographically remote domain z ( r , t ). We demonstrate the capacity of the RESP model by validating its ability to predict Colorado winter precipitation in a cross-validation study (Section 3). Our study represents a type of perfect prognosis problem in which future precipitation will be studied with co- variates that have been simulated by GCMs. Since atmospheric processes have relatively short memory, it is reasonable to assume winter precipitation is conditionally independent across years when local and remote covariates are given. Therefore, we develop the RESP model assuming there is no meaningful temporal dependence. We conclude with discus- sions of temporal extensions and other directions for future work and further application (Section 4). Teleconnection manifests as an aggregate property of spatially continuous covariates. For example, consider the sea surface temperature (SST) at location r and time t , z ( r , t ). In spatially varying coefficient models (1), it is common to adopt a teleconnection index z ( t ) ∈ R that is defined as the average SST z ( r , t ) over a region R ⊂ D$_{Z}$ . In (1), the spatially varying coefficient term z ( t ) θ ( s ) motivates the RESP model through the expansion z ( t ) θ ( s ) = 1 |R| ∫ R z ( r , t ) θ ( s ) d r . (2) 2 A geostatistical model for spatially remote covariates 5