Martingale approximations for sums of stationary processes

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dc.creatorWu, Wei Biao
dc.creatorWoodroofe, Michael
dc.date2004-10-06
dc.date.accessioned2026-07-07T05:12:58Z
dc.date.available2026-07-07T05:12:58Z
dc.descriptionApproximations to sums of stationary and ergodic sequences by martingales are investigated. Necessary and sufficient conditions for such sums to be asymptotically normal conditionally given the past up to time 0 are obtained. It is first shown that a martingale approximation is necessary for such normality and then that the sums are asymptotically normal if and only if the approximating martingales satisfy a Lindeberg-Feller condition. Using the explicit construction of the approximating martingales, a central limit theorem is derived for the sample means of linear processes. The conditions are not sufficient for the functional version of the central limit theorem. This is shown by an example, and a slightly stronger sufficient condition is given.
dc.descriptionPublished by the Institute of Mathematical Statistics (http://www.imstat.org) in the Annals of Probability (http://www.imstat.org/aop/) at http://dx.doi.org/10.1214/009117904000000351
dc.identifierhttps://arxiv.org/abs/math/0410160
dc.identifierhttp://arxiv.org/abs/math/0410160
dc.identifierAnnals of Probability 2004, Vol. 32, No. 2, 1674-1690
dc.identifierdoi:10.1214/009117904000000351
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72779
dc.subjectProbability
dc.subject60F17, 60G42, 60F05 (Primary) 60J10. (Secondary)
dc.titleMartingale approximations for sums of stationary processes
dc.typetext

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