Interpolation for second order stationary random fields: time domain recipe

Abstract

We consider a discrete time second order stationary random field and provide a time domain recipe for the interpolation based on the southwest and northeast corners. Our method is based on Salehi's approach, applying Von Neumann's celebrated alternative projection for-\break \noindent mula, but making a short cut by interpolating the innovations in the forward and backward moving average representations. We provide explicit expressions for the interpolator and error terms for the moving average random fields of finite order; for the MA($\boldsymbol {1}$) spatial model, we express the interpolator in terms of the observed values and the coefficients of the model. Following Kohli and Pourahmadi, we also derive the covariances between the present values and interpolation errors.