In this presentation, we will consider two different types of models: the threshold CIR process and the threshold CKLS process. These models are continuous-time process which is self-exciting. We study the asymptotic behavior of the maximum likelihood estimator of the drift parameters in the case of continuous time and discrete time observations of their trajecory. 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.
Based on joint works with Sara Mazzonetto.
