Title: Parameters estimation of a Threshold Chan-Karolyi-Longstaff-Sanders process from continuous and discrete observations Show Chinese title

Title: 基于连续和离散观测的阈值Chan-Karolyi-Longstaff-Sanders过程的参数估计

Abstract: We consider a continuous time process that is self-exciting and ergodic, called threshold Chan-Karolyi-Longstaff-Sanders (CKLS) process. This process is a generalization of various models in econometrics, such as Vasicek model, Cox-Ingersoll-Ross, and Black-Scholes, 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 considering (multiple) thresholds. Show Chinese abstract

Abstract: 我们研究了一个连续时间的自激发且遍历的过程，称为阈值 Chan-Karolyi-Longstaff-Sanders (CKLS) 过程。 该过程是计量经济学中多种模型的一般化，如 Vasicek 模型、Cox-Ingersoll-Ross 模型和 Black-Scholes 模型，允许存在多个阈值来决定动态变化。 我们研究了连续时间和离散时间观测情况下漂移参数的最大似然估计和准最大似然估计的渐近行为。 我们证明，在高频观测和无限时间范围的情况下，估计量满足与连续时间观测情况相同的渐近正态性性质。 我们还讨论了扩散系数的估计问题。 最后，我们将我们的估计器应用于模拟数据和真实数据，以激励考虑（多个）阈值。