IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v26y2005i6p825-842.html
   My bibliography  Save this article

Maximum Likelihood Estimation for a First‐Order Bifurcating Autoregressive Process with Exponential Errors

Author

Listed:
  • J. Zhou
  • I. V. Basawa

Abstract

. Exact and asymptotic distributions of the maximum likelihood estimator of the autoregressive parameter in a first‐order bifurcating autoregressive process with exponential innovations are derived. The limit distributions for the stationary, critical and explosive cases are unified via a single pivot using a random normalization. The pivot is shown to be asymptotically exponential for all values of the autoregressive parameter.

Suggested Citation

  • J. Zhou & I. V. Basawa, 2005. "Maximum Likelihood Estimation for a First‐Order Bifurcating Autoregressive Process with Exponential Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 825-842, November.
    • Handle: RePEc:bla:jtsera:v:26:y:2005:i:6:p:825-842
    DOI: 10.1111/j.1467-9892.2005.00440.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.2005.00440.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9892.2005.00440.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Davis, Richard A. & McCormick, William P., 1989. "Estimation for first-order autoregressive processes with positive or bounded innovations," Stochastic Processes and their Applications, Elsevier, vol. 31(2), pages 237-250, April.
    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. Bernard Bercu & Vassili Blandin, 2015. "Limit theorems for bifurcating integer-valued autoregressive processes," Statistical Inference for Stochastic Processes, Springer, vol. 18(1), pages 33-67, April.
    2. Bercu, Bernard & Blandin, Vassili, 2015. "A Rademacher–Menchov approach for random coefficient bifurcating autoregressive processes," Stochastic Processes and their Applications, Elsevier, vol. 125(4), pages 1218-1243.
    3. Zhang, Chenhua, 2011. "Parameter estimation for first-order bifurcating autoregressive processes with Weibull innovations," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1961-1969.
    4. de Saporta, Benoîte & Gégout-Petit, Anne & Marsalle, Laurence, 2014. "Statistical study of asymmetry in cell lineage data," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 15-39.
    5. S. Valère Bitseki Penda & Adélaïde Olivier, 2017. "Autoregressive functions estimation in nonlinear bifurcating autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 179-210, July.
    6. Hwang, S.Y. & Basawa, I.V., 2009. "Branching Markov processes and related asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1155-1167, July.
    7. Vincent Bansaye & S. Valère Bitseki Penda, 2021. "A Phase Transition for Large Values of Bifurcating Autoregressive Models," Journal of Theoretical Probability, Springer, vol. 34(4), pages 2081-2116, December.
    8. Terpstra, Jeff T. & Elbayoumi, Tamer, 2012. "A law of large numbers result for a bifurcating process with an infinite moving average representation," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 123-129.

    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. Allen, Michael R. & Datta, Somnath, 1999. "Estimation of the index parameter for autoregressive data using the estimated innovations," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 315-324, February.
    2. Vicky Fasen & Florian Fuchs, 2013. "Spectral estimates for high-frequency sampled continuous-time autoregressive moving average processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(5), pages 532-551, September.
    3. Zhang, Chenhua, 2011. "Parameter estimation for first-order bifurcating autoregressive processes with Weibull innovations," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1961-1969.
    4. Shu, Yin & Feng, Qianmei & Liu, Hao, 2019. "Using degradation-with-jump measures to estimate life characteristics of lithium-ion battery," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    5. Anders Eriksson & Daniel P. A. Preve & Jun Yu, 2019. "Forecasting Realized Volatility Using a Nonnegative Semiparametric Model," JRFM, MDPI, vol. 12(3), pages 1-23, August.
    6. Preve, Daniel & Medeiros, Marcelo C., 2011. "Linear programming-based estimators in simple linear regression," Journal of Econometrics, Elsevier, vol. 165(1), pages 128-136.
    7. Isabel Pereira & M. Antonia Amaral-Turkman, 2004. "Bayesian prediction in threshold autoregressive models with exponential white noise," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 45-64, June.
    8. Ching-Kang Ing & Chiao-Yi Yang, 2014. "Predictor Selection for Positive Autoregressive Processes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 243-253, March.
    9. Preve, Daniel, 2015. "Linear programming-based estimators in nonnegative autoregression," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 225-234.
    10. Brown, Tim C. & Feigin, Paul D. & Pallant, Diana L., 1996. "Estimation for a class of positive nonlinear time series models," Stochastic Processes and their Applications, Elsevier, vol. 63(2), pages 139-152, November.

    More about this item

    Statistics

    Access and download statistics

    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:bla:jtsera:v:26:y:2005:i:6:p:825-842. 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: Wiley-Blackwell Digital Licensing or Christopher F. Baum (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.