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July 2006 Central limit theorem for stationary linear processes
Magda Peligrad, Sergey Utev
Ann. Probab. 34(4): 1608-1622 (July 2006). DOI: 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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Magda Peligrad. Sergey Utev. "Central limit theorem for stationary linear processes." Ann. Probab. 34 (4) 1608 - 1622, July 2006.


Published: July 2006
First available in Project Euclid: 19 September 2006

zbMATH: 1101.60014
MathSciNet: MR2257658
Digital Object Identifier: 10.1214/009117906000000179

Primary: 60F05 , 60G10 , 60G42 , 60G48

Keywords: central limit theorem , ergodic theorem , martingale , stationary linear process

Rights: Copyright © 2006 Institute of Mathematical Statistics

Vol.34 • No. 4 • July 2006
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