REMOTE EFFECTS SPATIAL PROCESS MODELS the local response—i.e., in a continuous D$_{Z}$ s.t. D$_{Y}$ ∩ D$_{Z}$ =  . The RESP model is given by (3) Y ( s , t ) = x $^{T}$( s , t ) β + w ( s , t ) + ε ( s , t ) + γ ( s , t ) where the regression coefficients β ∈$_{R}$ $^{p}$, spatially correlated noise w ( s , t ), and independent noise ε ( s , t ) are standard components for spatial regression models (Banerjee et al., 2015, Chapters 6, 9, 11). In the RESP model the teleconnection effect given by γ ( s , t ) is defined by which describes the net effect of the remote covariates z ( r , t ) on the continuous spatial process Y ( s , t ) at discrete time t . The integral (4) reduces to a sum for finite samples, in which the remote covariates z ( r , t ) are observed at n$_{r}$ < ∞ locations. Multivariate extensions of (4) are discussed in Section 4. The remote (or teleconnection) coefficients α ( s , r ) are spatially correlated and doubly- indexed by ( s , r ) ∈ D$_{Y}$ × D$_{Z}$ . The spatial correlation and double-indexing of α ( s , r ) rep- resents teleconnection effects that vary regionally in the sense that the response Y ( s , t ) at one location s ∈ D$_{Y}$ can respond to the remote covariates z ( r , t ) more strongly than the response Y ( s $^{′}$, t ) at another location s ′ ∈ D$_{Y}$ . Similarly, the response Y ( s , t ) at one location s ∈ D$_{Y}$ can respond differently to remote covariates z ( r , t ) and z ( r $^{′}$, t ) at distinct remote locations r , r ′ ∈ D$_{Z}$ . Thus, the remote coefficients α ( s , r ) vary spatially and use the remote covariates z ( r , t ) to provide local adjustment to the mean response. The teleconnection term γ ( s , t ) is well defined because we assume the remote covariates z ( r , t ) are known and square-integrable over D$_{Z}$ at each time point t (Adler & Taylor, 2007, Section 5.2). The RESP model provides a simple geostatistical approach to modeling teleconnections by extending spatial regression models to incorporate data from spatially remote regions. The teleconnection term γ ( s , t ) distinguishes the RESP model (3) from standard geostatis- 7 (4) γ ( s , t ) = ∫ D$_{Z}$ z ( r , t ) α ( s , r ) d r