Central limit theorem for stationary linear processes
Open Access
- 1 July 2006
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 34 (4) , 1608-1622
- https://doi.org/10.1214/009117906000000179
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.Keywords
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