Central limit theorem for stationary linear processes
Probability
2007-05-23 v2
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.
Cite
@article{arxiv.math/0509682,
title = {Central limit theorem for stationary linear processes},
author = {Magda Peligrad and Sergey Utev},
journal= {arXiv preprint arXiv:math/0509682},
year = {2007}
}
Comments
Published at http://dx.doi.org/10.1214/009117906000000179 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)