REAL

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

Barczy, Mátyás and Ben Alaya, Mohamed and Kebaier, Ahmed and Pap, Gyula (2019) Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations. STATISTICS, 53 (3). pp. 533-568. ISSN 0233-1888

[img] Text
Barczy_BenAlaya_Kebaier_Pap_2019.pdf - Published Version
Restricted to Repository staff only

Download (2MB) | Request a copy
[img]
Preview
Text
Barczy_BenAlaya_Kebaier_Pap_2019_arxiv.pdf

Download (554kB) | Preview

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 behaviour of the MLE in question remains open.

Item Type: Article
Uncontrolled Keywords: stable Cox–Ingersoll–Ross process, maximum likelihood estimator, strong consistency, asymptotic mixed normality
Subjects: Q Science / természettudomány > QA Mathematics / matematika
Depositing User: Dr Mátyás Barczy
Date Deposited: 19 Sep 2019 08:33
Last Modified: 06 Apr 2023 07:23
URI: http://real.mtak.hu/id/eprint/99891

Actions (login required)

Edit Item Edit Item