Asymptotic results for spatial causal ARMA models
B. Gail Ivanoff and N.C. Weber
Source: Electron. J. Statist. Volume 4
(2010), 15-35.
Abstract
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.
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Keywords: Causal stationary processes; empirical distribution function; spatial ARMA processes; central limit theorem; quantile process; martingale
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Permanent link to this document: http://projecteuclid.org/euclid.ejs/1263305629
Digital Object Identifier: doi:10.1214/09-EJS533
Mathematical Reviews number (MathSciNet): MR2579552
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