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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Masuda, Hiroki¹ 

[1] Kyushu Univ, Fac Math, Nishi Ku, 744 Motooka, Fukuoka, Fukuoka 8190395, Japan

关键词: Asymptotic mixed normality;    High-frequency sampling;    Locally stable Levy process;    Stable quasi-likelihood function;    Stochastic differential equations;   

DOI  :  10.1016/j.spa.2018.04.004

来源: Elsevier

【 摘 要 】

We address estimation of parametric coefficients of a pure-jump Levy 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 Levy 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 Levy 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. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free