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- Title
Modified trajectory fitting estimators for multi‐regime threshold Ornstein–Uhlenbeck processes.
- Authors
Han, Yuecai; Zhang, Dingwen
- Abstract
The threshold Ornstein–Uhlenbeck process is a stochastic process governed by m Ornstein–Uhlenbeck subprocesses with the ith playing a role whenever the underlying process is in the ith regime. In this paper, we investigate the parameter estimation for threshold Ornstein–Uhlenbeck processes with multiple thresholds. The classical trajectory fitting method does not apply in this context due to the significantly complex calculations. Hence, a modified trajectory fitting method is used to obtain the explicit formula of the estimators for the drift parameters based on continuous observations. The strong consistency and asymptotic normality are proven. Simulation studies illustrate the asymptotic behaviour of the trajectory fitting estimators.
- Subjects
ORNSTEIN-Uhlenbeck process; ASYMPTOTIC normality; STOCHASTIC processes; PARAMETER estimation
- Publication
Stat, 2023, Vol 12, Issue 1, p1
- ISSN
2049-1573
- Publication type
Article
- DOI
10.1002/sta4.620