Central limit theorem for stationary linear processes

Details Central limit theorem for stationary linear processes Central limit theorem for stationary linear processes

2005-09-29

arxiv.org/abs/math/0509682v2

Annals of Probability 2006, Vol. 34, No. 4, 1608-1622

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000179 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000179

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.

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