Electronic Journal of Statistics

Asymptotic results for spatial causal ARMA models

B. Gail Ivanoff and N.C. Weber

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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.

Article information

Electron. J. Statist., Volume 4 (2010), 15-35.

First available in Project Euclid: 12 January 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G30: Order statistics; empirical distribution functions
Secondary: 60F17: Functional limit theorems; invariance principles 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 60G60: Random fields

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


Ivanoff, B. Gail; Weber, N.C. Asymptotic results for spatial causal ARMA models. Electron. J. Statist. 4 (2010), 15--35. doi:10.1214/09-EJS533. https://projecteuclid.org/euclid.ejs/1263305629

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See also

  • Related item: Ivanoff, B. G. and Weber, N. C. (2014). Corrigendum to “Asymptotic results for spatial causal ARMA models”. Electron. J. Statist. 8 1086–1087.