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.

翻译：我们用阈值Ornstein-Uhlenbeck 来参考一个连续时间阈值自动递减过程。 它沿循Ornstein-Uhlenbeck 动态, 当时间超过或低于固定水平时, 但在此水平( 阈值) 其系数可以不连续。 我们讨论( 准) — 最大可能性的漂移参数估计, 假设连续和离散的时间观察。 在ergodic 案例中, 我们得出这些测算器长期和高频率的一致和速度。 基于这些结果, 我们开发了在动态中存在阈值的测试。 最后, 我们将这些统计工具应用到短期利率模型中 。