Abstract: The threshold Ornstein-Uhlenbeck process is a continuous-time threshold autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above or below a fixed threshold, but its coefficients can be discontinuous at the threshold. We discuss (quasi)-maximum likelihood estimation of the drift parameters, assuming continuous and discrete time observations. In the ergodic case, we derive the consistency and the speed of convergence of these estimators in long time and high frequency. Based on these results, we develop a test for the presence of a threshold in the dynamics. Finally, we apply these statistical tools to short-term US interest rates modeling.

Key words and phrases: Interest rates, maximum likelihood, multi-threshold, regime-switching, self-exciting process, threshold diffusion, threshold Vasicek model.