Annals of Statistics
- Ann. Statist.
- Volume 35, Number 1 (2007), 355-392.
Volatility estimators for discretely sampled Lévy processes
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.
Ann. Statist., Volume 35, Number 1 (2007), 355-392.
First available in Project Euclid: 6 June 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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]
Aït-Sahalia, Yacine; Jacod, Jean. Volatility estimators for discretely sampled Lévy processes. Ann. Statist. 35 (2007), no. 1, 355--392. doi:10.1214/009053606000001190. https://projecteuclid.org/euclid.aos/1181100191