The Annals of Probability

Central limit theorem for stationary linear processes

Magda Peligrad and Sergey Utev

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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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Ann. Probab., Volume 34, Number 4 (2006), 1608-1622.

First available in Project Euclid: 19 September 2006

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Primary: 60F05: Central limit and other weak theorems 60G10: Stationary processes 60G42: Martingales with discrete parameter 60G48: Generalizations of martingales

Ergodic theorem central limit theorem stationary linear process martingale


Peligrad, Magda; Utev, Sergey. Central limit theorem for stationary linear processes. Ann. Probab. 34 (2006), no. 4, 1608--1622. doi:10.1214/009117906000000179.

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