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Asymptotic Normality for Weighted Sums of Linear Processes


  • K.M. Abadir

    (Imperial College London, UK)

  • W. Distaso

    (Imperial College London, UK)

  • L. Giraitis

    (Queen Mary, University of London, UK)

  • H.L. Koul

    (Michigan State University, USA)


We establish asymptotic normality of weighted sums of stationary linear processes with general triangular array weights and when the innovations in the linear process are martingale differences. The results are obtained under minimal conditions on the weights and as long as the process of conditional variances of innovations is covariance stationary with lag k auto-covariances tending to zero, as k tends to infinity. We also obtain weak convergence of weighted partial sum processes. The results are applicable to linear processes that have short or long memory or exhibit seasonal long memory behavior. In particular they are applicable to GARCH and ARCH(∞) models. They are also useful in deriving asymptotic normality of kernel estimators of a nonparametric regression function when errors may have long memory.

Suggested Citation

  • K.M. Abadir & W. Distaso & L. Giraitis & H.L. Koul, 2012. "Asymptotic Normality for Weighted Sums of Linear Processes," Working Paper series 23_12, Rimini Centre for Economic Analysis.
  • Handle: RePEc:rim:rimwps:23_12

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    Cited by:

    1. Liudas Giraitis & Donatas Surgailis & Andrius Škarnulis, 2015. "Integrated ARCH, FIGARCH and AR Models: Origins of Long Memory," Working Papers 766, Queen Mary University of London, School of Economics and Finance.
    2. Zhang, Li-Xin & Zhang, Yang, 2015. "Asymptotics for a class of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 47-56.
    3. Liudas Giraitis & George Kapetanios & Tony Yates, 2015. "Inference on Multivariate Heteroscedastic Time Varying Random Coefficient Models," Working Papers 767, Queen Mary University of London, School of Economics and Finance.

    More about this item


    Linear process; weighted sum; Lindeberg-Feller;

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