The Annals of Probability

Central limit theorem for stationary linear processes

Magda Peligrad and Sergey Utev

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Abstract

We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. Probab. 5 (1977) 616–621] and motivated by Gordin [Soviet Math. Dokl. 10 (1969) 1174–1176]. In doing so we shall preserve the generality of the coefficients, including the long range dependence case, and we shall express the variance of partial sums in a form easy to apply. Ergodicity is not required.

Article information

Source
Ann. Probab. Volume 34, Number 4 (2006), 1608-1622.

Dates
First available in Project Euclid: 19 September 2006

Permanent link to this document
http://projecteuclid.org/euclid.aop/1158673330

Digital Object Identifier
doi:10.1214/009117906000000179

Mathematical Reviews number (MathSciNet)
MR2257658

Zentralblatt MATH identifier
1101.60014

Subjects
Primary: 60F05: Central limit and other weak theorems 60G10: Stationary processes 60G42: Martingales with discrete parameter 60G48: Generalizations of martingales

Keywords
Ergodic theorem central limit theorem stationary linear process martingale

Citation

Peligrad, Magda; Utev, Sergey. Central limit theorem for stationary linear processes. Ann. Probab. 34 (2006), no. 4, 1608--1622. doi:10.1214/009117906000000179. http://projecteuclid.org/euclid.aop/1158673330.


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