Drift estimation for a Lévy-driven Ornstein–Uhlenbeck process with heavy tails

Alexander Gushchin, Ilya Pavlyukevich () and Marian Ritsch ()
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Ilya Pavlyukevich: Friedrich Schiller University Jena
Marian Ritsch: Friedrich Schiller University Jena

Statistical Inference for Stochastic Processes, 2020, vol. 23, issue 3, No 4, 553-570

Abstract: Abstract We consider the problem of estimation of the drift parameter of an ergodic Ornstein–Uhlenbeck type process driven by a Lévy process with heavy tails. The process is observed continuously on a long time interval [0, T], $$T\rightarrow \infty $$ T → ∞ . We prove that the statistical model is locally asymptotic mixed normal and the maximum likelihood estimator is asymptotically efficient.

Keywords: Lévy process; Ornstein–Uhlenbeck type process; Local asymptotic mixed normality; Heavy tails; Regular variation; Maximum likelihood estimator; Asymptotic observed information; 62M05; 60F05; 60J75 (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sistpr:v:23:y:2020:i:3:d:10.1007_s11203-020-09210-8

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DOI: 10.1007/s11203-020-09210-8

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