We consider a continuous-time process which is self-exciting and ergodic, called threshold Chan–Karolyi–Longstaff–Sanders (CKLS) process. We allow for the presence of several thresholds which determine changes in the dynamics. We study the asymptotic behavior of the maximum 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 discuss diffusion coefficient estimation as well. Finally, we apply our estimators to simulated and real data to motivate considering (multiple) thresholds.