Magda Peligrad, Sergey Utev
Published 2005-09-29, updated 2006-09-25Version 2
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.
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)
Journal: Annals of Probability 2006, Vol. 34, No. 4, 1608-1622
Exactness of martingale approximation and the central limit theorem
A strictly stationary, "causal," 5-tuplewise independent counterexample to the central limit theorem
Central limit theorem for sampled sums of dependent random variables
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