Electronic Journal of Statistics

Asymptotic results for spatial causal ARMA models

B. Gail Ivanoff and N.C. Weber

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 12 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1263305629

Digital Object Identifier
doi:10.1214/09-EJS533

Mathematical Reviews number (MathSciNet)
MR2579552

Zentralblatt MATH identifier
1298.62075

Subjects
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

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

Citation

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.