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

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 b...

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Bibliographic Details
Published in:Statistics & probability letters 2016-10, Vol.117, p.12-22
Main Authors: Álvarez-Liébana, Javier, Bosq, Denis, Ruiz-Medina, María D.
Format: Article
Language:English
Subjects:
Autoregressive Hilbertian processes
Banach-valued autoregressive processes
Consistency
Maximum likelihood parameter estimator
Ornstein–Uhlenbeck process
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Summary: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.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2016.04.023