  We refer by threshold Ornstein-Uhlenbeck to a continuous-time threshold
autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above
or below a fixed level, yet at this level (threshold) its coefficients can be
discontinuous. We discuss (quasi)-maximum likelihood estimation of the drift
parameters, both assuming continuous and discrete time observations. In the
ergodic case, we derive consistency and 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.
