IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v81y2011i8p1104-1111.html
   My bibliography  Save this article

Estimation for discretely observed continuous state branching processes with immigration

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715211000873
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Overbeck, Ludger & Rydén, Tobias, 1997. "Estimation in the Cox-Ingersoll-Ross Model," Econometric Theory, Cambridge University Press, vol. 13(3), pages 430-461, June.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Pap Gyula & Szabó Tamás T., 2016. "Change detection in the Cox–Ingersoll–Ross model," Statistics & Risk Modeling, De Gruyter, vol. 33(1-2), pages 21-40, September.
    5. 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.
    6. Matyas Barczy & Leif Doering & Zenghu Li & Gyula Pap, 2012. "On parameter estimation for critical affine processes," Papers 1210.1866, arXiv.org, revised Mar 2013.
    7. Matyas Barczy & Gyula Pap, 2013. "Asymptotic properties of maximum likelihood estimators for Heston models based on continuous time observations," Papers 1310.4783, arXiv.org, revised Jun 2015.
    8. Zani, Marguerite, 2002. "Large deviations for squared radial Ornstein-Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 25-42, November.
    9. Matyas Barczy & Leif Doering & Zenghu Li & Gyula Pap, 2013. "Parameter estimation for a subcritical affine two factor model," Papers 1302.3451, arXiv.org, revised Apr 2014.
    10. Xu, Wei, 2014. "Parameter estimation in two-type continuous-state branching processes with immigration," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 124-134.
    11. Jonas Vogt, 2017. "Doubly Stochastic Reduced Form Credit Risk Model and Default Probability Uncertainty – a Technical Toolkit," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 6(2), pages 1-2.
    12. Cleur, Eugene M & Manfredi, Piero, 1999. "One Dimensional SDE Models, Low Order Numerical Methods and Simulation Based Estimation: A Comparison of Alternative Estimators," Computational Economics, Springer;Society for Computational Economics, vol. 13(2), pages 177-197, April.
    13. Erik Lindström, 2007. "Estimating parameters in diffusion processes using an approximate maximum likelihood approach," Annals of Operations Research, Springer, vol. 151(1), pages 269-288, April.
    14. Nikolaos Limnios & Elena Yarovaya, 2020. "Diffusion Approximation of Branching Processes in Semi-Markov Environment," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1583-1590, December.
    15. Robert Jung & Gerd Ronning & A. Tremayne, 2005. "Estimation in conditional first order autoregression with discrete support," Statistical Papers, Springer, vol. 46(2), pages 195-224, April.
    16. Matyas Barczy & Mohamed Ben Alaya & Ahmed Kebaier & Gyula Pap, 2017. "Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations," Papers 1711.02140, arXiv.org, revised Feb 2019.
    17. Demni, N. & Zani, M., 2009. "Large deviations for statistics of the Jacobi process," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 518-533, February.
    18. Nicole Hufnagel & Jeannette H. C. Woerner, 2022. "Martingale estimation functions for Bessel processes," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 337-353, July.
    19. Yong-Hua Mao & Yan-Hong Song, 2022. "Criteria for Geometric and Algebraic Transience for Discrete-Time Markov Chains," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1974-2008, September.
    20. Beáta Bolyog & Gyula Pap, 2019. "On conditional least squares estimation for affine diffusions based on continuous time observations," Statistical Inference for Stochastic Processes, Springer, vol. 22(1), pages 41-75, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1104-1111. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.