Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations

Abstract

We consider a stable Cox--Ingersoll--Ross process driven by a standard Wiener process and a spectrally positive strictly stable Lévy process, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate based on continuous time observations. We distinguish three cases: subcritical, critical and supercritical. In all cases we prove strong consistency of the MLE in question, in the subcritical case asymptotic normality, and in the supercritical case asymptotic mixed normality are shown as well. In the critical case the description of the asymptotic behavior of the MLE in question remains open.

arXiv comment47 pages. In Appendices we recall some notions and statements from arXiv:1509.08869 and arXiv:1609.05865