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≥0ai,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.
"Asymptotic results for spatial causal ARMA models." Electron. J. Statist. 4 15 - 35, 2010. https://doi.org/10.1214/09-EJS533