Central limit theorem for stationary linear processes
Magda Peligrad and Sergey Utev
Source: Ann. Probab. Volume 34, Number 4
(2006), 1608-1622.
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.
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Permanent link to this document: http://projecteuclid.org/euclid.aop/1158673330
Digital Object Identifier: doi:10.1214/009117906000000179
Mathematical Reviews number (MathSciNet): MR2257658
Zentralblatt MATH identifier: 1101.60014
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