Parameters estimation of a threshold Chan–Karolyi–Longstaff–Sanders process from continuous and discrete observations

We consider a continuous time process that is self‐exciting and ergodic, called the threshold Chan–Karolyi–Longstaff–Sanders (CKLS) process. This process is a generalization of various models in econometrics, such as the Vasicek model, the Cox–Ingersoll–Ross model, and the Black–Scholes model, allowing for the presence of several thresholds which determine changes in the dynamics. We study the asymptotic behavior of maximum‐likelihood and quasi‐maximum‐likelihood estimators of the drift parameters in the case of continuous time and discrete time observations. We show that for high frequency observations and infinite horizon the estimators satisfy the same asymptotic normality property as in the case of continuous time observations. We also discuss diffusion coefficient estimation. Finally, we apply our estimators to simulated and real data to motivate the consideration of (multiple) thresholds.