Modified trajectory fitting estimators for multi‐regime threshold Ornstein–Uhlenbeck processes

Abstract

The threshold Ornstein–Uhlenbeck process is a stochastic process governed by Ornstein–Uhlenbeck subprocesses with the th playing a role whenever the underlying process is in the th 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.