Drift estimation of the threshold Ornstein-Uhlenbeck process from continuous and discrete observations

TL;DR

This paper develops methods for estimating the drift parameters of a threshold Ornstein-Uhlenbeck process from continuous and discrete data, including consistency, convergence rates, and a threshold presence test, with applications to US interest rates.

Contribution

It introduces (quasi)-maximum likelihood estimators for the threshold Ornstein-Uhlenbeck process and analyzes their properties, including a new test for threshold detection.

Findings

Establishes consistency and convergence rates of estimators.

Develops a statistical test for the existence of a threshold.

Applies methods to real US interest rate data.

Abstract

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.