Open Access
2010 Asymptotic results for spatial causal ARMA models
B. Gail Ivanoff, N.C. Weber
Electron. J. Statist. 4: 15-35 (2010). DOI: 10.1214/09-EJS533


The paper establishes a functional central limit theorem for the empirical distribution function of a stationary, causal, ARMA process given by Xs,t=i0j0ai,j ξsi,tj, (s,t)Z2, where the ξi,j are independent and identically distributed, zero mean innovations. By judicious choice of σfields and element enumeration, one dimensional martingale arguments are employed to establish the result.


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B. Gail Ivanoff. N.C. Weber. "Asymptotic results for spatial causal ARMA models." Electron. J. Statist. 4 15 - 35, 2010.


Published: 2010
First available in Project Euclid: 12 January 2010

zbMATH: 1298.62075
MathSciNet: MR2579552
Digital Object Identifier: 10.1214/09-EJS533

Primary: 62G30
Secondary: 60F17 , 60G60 , 62M10

Keywords: Causal stationary processes , central limit theorem , Empirical distribution function , martingale , quantile process , spatial ARMA processes

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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