The Annals of Probability

Central limit theorem for linear processes

Magda Peligrad and Sergey Utev

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Abstract

In this paper we study the CLT for partial sums of a generalized linear process $X_n = \sum_{i=1}^n a_{ni} \xi_i$, where $\sup_n \sum_{i=1}^n a_{ni}^2 < \infty, \max_{1 \leq i \leq n}are in turn, pairwise mixing martingale differences, mixing sequences or associated sequences. The results are important in analyzing the asymptotical properties of some estimators as well as of linear processes.

Article information

Source
Ann. Probab., Volume 25, Number 1 (1997), 443-456.

Dates
First available in Project Euclid: 18 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1024404295

Digital Object Identifier
doi:10.1214/aop/1024404295

Mathematical Reviews number (MathSciNet)
MR1428516

Zentralblatt MATH identifier
0876.60013

Subjects
Primary: 60G09: Exchangeability 60F05: Central limit and other weak theorems

Keywords
Linear process dependent random variables central limit theorem

Citation

Peligrad, Magda; Utev, Sergey. Central limit theorem for linear processes. Ann. Probab. 25 (1997), no. 1, 443--456. doi:10.1214/aop/1024404295. https://projecteuclid.org/euclid.aop/1024404295


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  • CINCINNATI, OHIO 45221-0025 AND DEPARTMENT OF MATHEMATICS AND STATISTICS LATROBE UNIVERSITY
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