Asymptotic results for spatial causal ARMA models

Abstract

The paper establishes a functional central limit theorem for the empirical distribution function of a stationary, causal, ARMA process given by X_s,t=∑_i≥0∑_j≥0a_i,j ξ_s−i,t−j, (s,t)∈Z², 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.