Parameter estimation for Ornstein–Uhlenbeck processes of the second kind driven by α-stable Lévy motions

ABSTRACT

In this article, we study the problem of parameter estimation for Ornstein–Uhlenbeck processes of the second kind driven by α-stable Lévy motions, based on continuous and discrete observations, respectively. Using the trajectory fitting method combined with the weighted least-squares technique, we discuss the consistency and the asymptotic distributions of the estimators for general weights in both the ergodic and the non ergodic cases.

KEYWORDS:

• α-Stable Lévy motions
• Asymptotic distribution
• Consistency
• Ornstein–Uhlenbeck processes
• Weighted trajectory fitting estimator.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60G52
• 65C30
• 93E24

Acknowledgments

The authors are very grateful to the editor and the anonymous referees for their insightful and valuable comments, which have improved the presentation of the article. The authors would like to thank Professor Shibin Zhang, because he gave us the R functions of stable random variable.

Funding

Qian Yu was supported by the National Natural Science Foundation of China (11501009). Guangjun Shen was supported by the National Natural Science Foundation of China (11271020) and the Distinguished Young Scholars Foundation of Anhui Province (1608085J06) and the Top Talent Project of University Discipline (Speciality) (gxbjZD03), Mingxiang Cao was supported by the National Natural Science Foundation of China (11601008).