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

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  • Li, Zenghu
  • Ma, Chunhua

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.

Suggested Citation

  • Li, Zenghu & Ma, Chunhua, 2015. "Asymptotic properties of estimators in a stable Cox–Ingersoll–Ross model," Stochastic Processes and their Applications, Elsevier, vol. 125(8), pages 3196-3233.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:8:p:3196-3233
    DOI: 10.1016/j.spa.2015.03.002
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    11. Martin Friesen & Peng Jin & Jonas Kremer & Barbara Rüdiger, 2023. "Regularity of transition densities and ergodicity for affine jump‐diffusions," Mathematische Nachrichten, Wiley Blackwell, vol. 296(3), pages 1117-1134, March.
    12. Mátyás Barczy & Kristóf Körmendi & Gyula Pap, 2016. "Statistical inference for critical continuous state and continuous time branching processes with immigration," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(7), pages 789-816, October.
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    15. Yurong Pan & Litan Yan, 2019. "The Least Squares Estimation for the α-Stable Ornstein-Uhlenbeck Process with Constant Drift," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1165-1182, December.
    16. Fontana, Claudio & Gnoatto, Alessandro & Szulda, Guillaume, 2023. "CBI-time-changed Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 323-349.
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