Asymptotic properties of estimators in a stable Cox-Ingersoll-Ross model

Abstract

We study the estimation of a stable Cox-Ingersoll-Ross model, which is a special subcritical continuous-state branching process with immigration. The process is characterized in terms of some stochastic equations. The exponential ergodicity and strong mixing property of the process and the heavy tail behavior of some related random sequences are studied. We also establish the convergence of some point processes and partial sums associated with the model. From those results, we derive the consistency and central limit theorems of the conditional least squares estimators and the weighted conditional least squares estimators of the drift parameters based on low frequency observations. A weakly consistent estimator is also proposed for the volatility coefficient based on high frequency observations.

References in corpus (2)

• Basic Properties of Strong Mixing Conditions. A Survey and Some Open Questions
• Stable limits of martingale transforms with application to the estimation of GARCH parameters

Cited by in corpus (7)

• Parameter Estimation in Two-type Continuous-state Branching Processes with Immigration
• Local asymptotic quadraticity of statistical experiments connected with a Heston model
• Statistical inference for critical continuous state and continuous time branching processes with immigration
• Statistical inference for 2-type doubly symmetric critical irreducible continuous state and continuous time branching processes with immigration
• Nonparametric Estimation for Jump-Diffusion CIR Model
• Positive Harris recurrence and exponential ergodicity of the basic affine jump-diffusion
• Sample paths of continuous-state branching processes with dependent immigration