On the prediction of vector-valued random fields and the spectral distribution of their evanescent component

Let (Xm,n)(m,n)∈Z2 be a Cp-valued wide sense stationary process. We study the prediction theory of such processes according to different total orders on Z2. In the case of a “rational order”, we give the spectral distribution of the resulting evanescent component and prove that for two different rational orders, the resulting evanescent components are mutually orthogonal.