Parameters estimation of a Threshold CKLS process from continuous and discrete observations

Sara Mazzonetto (1, 2) , Benoît Nieto (3, 4, 5)

1 PASTA - Processus aléatoires spatio-temporels et leurs applications
2 IECL - Institut Élie Cartan de Lorraine
3 ICJ - Institut Camille Jordan
4 ECL - École Centrale de Lyon
5 PSPM - Probabilités, statistique, physique mathématique

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.

Mots clés: CIR; CKLS; maximum likelihood; regime-switch; self-exciting process; threshold diffusion

Domaines: Probabilités [math.PR]; Statistiques [math.ST]

Sara Mazzonetto, Benoît Nieto. Parameters estimation of a Threshold CKLS process from continuous and discrete observations. 2024. ⟨hal-04524431⟩