Central limit theorem for stationary linear processes

Preprint

25 September 2006

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0509682

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.

Keywords

CENTRAL LIMIT THEOREM
INCLUDING MARTINGALES
STATIONARY LINEAR
LINEAR PROCESSES
LIMIT THEOREM
INNOVATIONS
SOVIET MATH
MOTIVATED
ANN

All Related Versions

Version 1, 2005-09-29, ArXiv
Version 2, 2006-09-25, ArXiv
Published version: The Annals of Probability, 34 (4), 1608.

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