Asymptotic results for spatial causal ARMA models

作者：Ivanoff B Gail^*; Weber N C

来源：Electronic Journal of Statistics, 2010, 4(none): 15-35.

DOI：10.1214/09-EJS533

• Causal stationary processes
• empirical distribution function
• spatial ARMA processes
• central limit theorem
• quantile process
• martingale

The paper establishes a functional central limit theorem for the empirical distribution function of a stationary, causal, ARMA process given by X-s,X-t = Sigma(i >= 0) Sigma(j >= 0) a(i,j) xi(s-i),(t-j), (s, t) is an element of Z(2), where the xi(i,j) areindependent and identically distributed, zero mean innovations. By judicious choice of sigma-fields and element enumeration, one dimensional martingale arguments are employed to establish the result.

• 出版日期2010