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Quasi-maximum likelihood estimation of long-memory linear processes

Author

Listed:
  • Jean-Marc Bardet

    (University Panthéon-Sorbonne)

  • Yves Gael Tchabo MBienkeu

    (University Panthéon-Sorbonne)

Abstract

The purpose of this paper is to study the convergence of the quasi-maximum likelihood (QML) estimator for long memory linear processes. We first establish a correspondence between the long-memory linear process representation and the long-memory AR $$(\infty )$$ ( ∞ ) process representation. We then establish the almost sure consistency and asymptotic normality of the QML estimator. Numerical simulations illustrate the theoretical results and confirm the good performance of the estimator.

Suggested Citation

  • Jean-Marc Bardet & Yves Gael Tchabo MBienkeu, 2024. "Quasi-maximum likelihood estimation of long-memory linear processes," Statistical Inference for Stochastic Processes, Springer, vol. 27(3), pages 457-483, October.
    • Handle: RePEc:spr:sistpr:v:27:y:2024:i:3:d:10.1007_s11203-024-09313-6
    DOI: 10.1007/s11203-024-09313-6
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    References listed on IDEAS

    as
    1. Bardet, Jean-Marc & Tudor, Ciprian, 2014. "Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 1-16.
    2. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
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