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

By Zenghu Li, Chunhua Ma. 2013

118 citations recorded by the source corpus.

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.

Subfields: Finance, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/118ef7b97d50ef7e81c213cb058595bf535bedf1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Zenghu Li
2. Chunhua Ma

In Mathematical Physics

1. Zenghu Li
2. Amaury Lambert
3. Chunhua Ma
4. Gyula Pap
5. Mátyás Barczy
6. Martin Keller‐Ressel

In Statistics and Probability

1. Zenghu Li
2. Amaury Lambert
3. Chunhua Ma
4. Martin Keller‐Ressel

Citations in the corpus

• Continuous-State Branching Processes with Immigration (2019, methodology): “It has played an important role in the study of asymptotics of the estimators for the α-stable CIR-model in Li and Ma (2015).”