Asymptotic results for spatial causal ARMA models

The paper establishes a functional central limit theorem for the empirical distribution function of a stationary, causal, ARMA process given by Xs,t = i≥0 j≥0 a i,j ξ s−i,t−j , (s, t) ∈ Z 2 , where the ξ i,j are independent and identically distributed, zero mean innovations. By judicious choice of σ−fields and element enumeration, one dimensional martingale arguments are employed to establish the result.