Non-Gaussian quasi-likelihood estimation of SDE driven by locally stable Lévy process

Hiroki Masuda

Stochastic Processes and their Applications, 2019, vol. 129, issue 3, 1013-1059

Abstract: We address estimation of parametric coefficients of a pure-jump Lévy driven univariate stochastic differential equation (SDE) model, which is observed at high frequency over a fixed time period. It is known from the previous study (Masuda, 2013) that adopting the conventional Gaussian quasi-maximum likelihood estimator then leads to an inconsistent estimator. In this paper, under the assumption that the driving Lévy process is locally stable, we extend the Gaussian framework into a non-Gaussian counterpart, by introducing a novel quasi-likelihood function formally based on the small-time stable approximation of the unknown transition density. The resulting estimator turns out to be asymptotically mixed normally distributed without ergodicity and finite moments for a wide range of the driving pure-jump Lévy processes, showing much better theoretical performance compared with the Gaussian quasi-maximum likelihood estimator. Extensive simulations are carried out to show good estimation accuracy. The case of large-time asymptotics under ergodicity is briefly mentioned as well, where we can deduce an analogous asymptotic normality result.

Keywords: Asymptotic mixed normality; High-frequency sampling; Locally stable Lévy process; Stable quasi-likelihood function; Stochastic differential equations (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:3:p:1013-1059

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DOI: 10.1016/j.spa.2018.04.004

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