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Consistency of the plug-in functional predictor of the Ornstein–Uhlenbeck process in Hilbert and Banach spaces

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  • Álvarez-Liébana, Javier
  • Bosq, Denis
  • Ruiz-Medina, María D.

Abstract

New results on functional prediction of the Ornstein–Uhlenbeck process in an autoregressive Hilbert-valued and Banach-valued frameworks are derived. Specifically, consistency of the maximum likelihood estimator of the autocorrelation operator, and of the associated plug-in predictor is obtained in both frameworks.

Suggested Citation

  • Álvarez-Liébana, Javier & Bosq, Denis & Ruiz-Medina, María D., 2016. "Consistency of the plug-in functional predictor of the Ornstein–Uhlenbeck process in Hilbert and Banach spaces," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 12-22.
    • Handle: RePEc:eee:stapro:v:117:y:2016:i:c:p:12-22
    DOI: 10.1016/j.spl.2016.04.023
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    References listed on IDEAS

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    Cited by:

    1. Ruiz-Medina, María D. & Álvarez-Liébana, Javier, 2019. "Strongly consistent autoregressive predictors in abstract Banach spaces," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 186-201.
    2. Ruiz-Medina, M.D. & Álvarez-Liébana, J., 2019. "A note on strong-consistency of componentwise ARH(1) predictors," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 224-228.

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