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Optimal stable Ornstein–Uhlenbeck regression

Japanese Journal of Statistics and Data Science, ISSN: 2520-8764, Vol: 6, Issue: 1, Page: 573-605
2023
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Article Description

We prove asymptotically efficient inference results concerning an Ornstein–Uhlenbeck regression model driven by a non-Gaussian stable Lévy process, where the output process is observed at high frequency over a fixed period. The local asymptotics of non-ergodic type for the likelihood function is presented, followed by a way to construct an asymptotically efficient estimator through a suboptimal, yet very simple preliminary estimator.

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