Annals of Statistics

Volatility estimators for discretely sampled Lévy processes

Yacine Aït-Sahalia and Jean Jacod

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This paper studies the estimation of the volatility parameter in a model where the driving process is a Brownian motion or a more general symmetric stable process that is perturbed by another Lévy process. We distinguish between a parametric case, where the law of the perturbing process is known, and a semiparametric case, where it is not. In the parametric case, we construct estimators which are asymptotically efficient. In the semiparametric case, we can obtain asymptotically efficient estimators by sampling at a sufficiently high frequency, and these estimators are efficient uniformly in the law of the perturbing process.

Article information

Ann. Statist., Volume 35, Number 1 (2007), 355-392.

First available in Project Euclid: 6 June 2007

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Zentralblatt MATH identifier

Primary: 62F12: Asymptotic properties of estimators 62M05: Markov processes: estimation
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60J60: Diffusion processes [See also 58J65]

Jumps efficiency inference discrete sampling


Aït-Sahalia, Yacine; Jacod, Jean. Volatility estimators for discretely sampled Lévy processes. Ann. Statist. 35 (2007), no. 1, 355--392. doi:10.1214/009053606000001190.

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