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Estimation for discretely observed continuous state branching processes with immigration

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  • Huang, Jianhui
  • Ma, Chunhua
  • Zhu, Cai

Abstract

We study the problem of parameter estimation for the continuous state branching processes with immigration, observed at discrete time points. The weighted conditional least square estimators (WCLSEs) are used for the drift parameters. Under the proper moment conditions, asymptotic distributions of the WCLSEs are obtained in the supercritical, sub- or critical cases.

Suggested Citation

  • Huang, Jianhui & Ma, Chunhua & Zhu, Cai, 2011. "Estimation for discretely observed continuous state branching processes with immigration," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1104-1111, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1104-1111
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    References listed on IDEAS

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    1. Ludger Overbeck, 1998. "Estimation for Continuous Branching Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 111-126, March.
    2. Overbeck, Ludger & Rydén, Tobias, 1997. "Estimation in the Cox-Ingersoll-Ross Model," Econometric Theory, Cambridge University Press, vol. 13(3), pages 430-461, June.
    3. Wei, C. Z. & Winnicki, J., 1989. "Some asymptotic results for the branching process with immigration," Stochastic Processes and their Applications, Elsevier, vol. 31(2), pages 261-282, April.
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    1. Barczy, Mátyás & Körmendi, Kristóf & Pap, Gyula, 2015. "Statistical inference for 2-type doubly symmetric critical irreducible continuous state and continuous time branching processes with immigration," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 92-123.
    2. Matyas Barczy & Leif Doering & Zenghu Li & Gyula Pap, 2012. "On parameter estimation for critical affine processes," Papers 1210.1866, arXiv.org, revised Mar 2013.
    3. 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.
    4. Matyas Barczy & Mohamed Ben Alaya & Ahmed Kebaier & Gyula Pap, 2016. "Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations," Papers 1609.05865, arXiv.org, revised Aug 2017.
    5. 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.
    6. Barczy, Mátyás & Ben Alaya, Mohamed & Kebaier, Ahmed & Pap, Gyula, 2018. "Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1135-1164.

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