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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Li, Zenghu¹  Ma, Chunhua^2,3 

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[2] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

关键词: Stable Cox-Ingersoll-Ross model;    Conditional least squares estimators;    Weighted conditional least squares estimators;    Branching process with immigration;    Exponential ergodicity;    Strong mixing property;   

DOI  :  10.1016/j.spa.2015.03.002

来源: Elsevier

【 摘 要 】

We study the estimation of a stable Cox-Ingersoll-Ross model, which is a special subcritical continuous-state branching process with immigration. The exponential ergodicity and strong mixing property of the process are proved by a coupling method. The regular variation properties of distributions of the model are studied. The key is to 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 (CLSEs) and the weighted conditional least squares estimators (WCLSEs) of the drift parameters based on low frequency observations. The theorems show that the WCLSEs are more efficient than the CLSEs and their errors have distinct decay rates n(-(alpha-1)/alpha) and n(-(alpha-1)/alpha 2), respectively, as the sample sizes n goes to infinity. The arguments depend heavily on the recent results on the construction and characterization of the model in terms of stochastic equations. (C) 2015 Elsevier B.V. All rights reserved.

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