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 Xs, t = Σi≥0 Σj≥0 ai, j ξs−i, t−j, (s, t) ∈ Z2, where the ξi, 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. © 2010, Institute of Mathematical Statistics. All rights reserved.