Two methods of estimation of the drift parameters of the Cox–Ingersoll–Ross process: Continuous observations

Olena Dehtiar, Yuliya Mishura and Kostiantyn Ralchenko

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 19, 6818-6833

Abstract: We consider a stochastic differential equation of the form drt=(a−brt)dt+σrtdWt, where a, b and σ are positive constants. The solution corresponds to the Cox–Ingersoll–Ross process. We study the estimation of an unknown drift parameter (a, b) by continuous observations of a sample path {rt,t∈[0,T]}. First, we prove the strong consistency of the maximum likelihood estimator. Since this estimator is well-defined only in the case 2a>σ2, we propose another estimator that is defined and strongly consistent for all positive a, b, σ. The quality of the estimators is illustrated by simulation results.

Date: 2022
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DOI: 10.1080/03610926.2020.1866611

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