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

Zenghu Li and Chunhua Ma

Stochastic Processes and their Applications, 2015, vol. 125, issue 8, 3196-3233

Abstract: 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−(α−1)/α and n−(α−1)/α2, 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.

Keywords: Stable Cox–Ingersoll–Ross model; Conditional least squares estimators; Weighted conditional least squares estimators; Branching process with immigration; Exponential ergodicity; Strong mixing property (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (20)

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DOI: 10.1016/j.spa.2015.03.002

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