Two methods of estimation of the drift parameters of the\n Cox-Ingersoll-Ross process: continuous observations

2020/05/11 by Olena Dehtiar, Dehtiar, Olena, Yuliya Mishura +3 · 3 citations
Economics, Econometrics and Finance · Mathematics · #60G22 #60H10 #62F10 #Complex Systems and Time Series Analysis #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2005.05262

openalex publication_date 2020/05/11 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We consider a stochastic differential equation of the form dr_t = (a - b\nr_t) dt + \σ\√(r_t)dW_t, where a, b and \σ are positive\nconstants. The solution corresponds to the Cox-Ingersoll-Ross process. We study\nthe estimation of an unknown drift parameter (a,b) by continuous observations\nof a sample path r_t,t\∈[0,T] . First, we prove the strong consistency of\nthe maximum likelihood estimator. Since this estimator is well-defined only in\nthe case 2a>\σ², we propose another estimator that is defined and\nstrongly consistent for all positive a, b, \σ. The quality of the\nestimators is illustrated by simulation results.\n

Cited by

• From CKLS Process to CIR-type and OU-type Processes: Using a Twice-differentiable Mapping and Generalized Girsanov's Theorem
• Estimation of the elasticity for CKLS model from high-frequency observations
• An Accurate Discretized Approach to Parameter Estimation in the CKLS Model via the CIR Framework

Related

• Parameter estimation in CKLS model by continuous observations
• Inference in the stochastic Cox-Ingersol-Ross diffusion process with continuous sampling: Computational aspects and simulation
• Asymptotic properties of estimators in a stable Cox-Ingersoll-Ross model
• A pathwise inference method for the parameters of diffusion terms
• Sharp large deviations for the drift parameter of the explosive Cox-Ingersoll-Ross process