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Least-squares estimation for bifurcating autoregressive processes

Author

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  • Zhou, J.
  • Basawa, I.V.

Abstract

Bifurcating autoregressive processes are used to model each line of descent in a binary tree as a standard AR(p) process, allowing for correlations between nodes which share the same parent. Limit distributions of the least-squares estimators of the model parameters for a pth-order bifurcating autoregressive process (BAR(p)) are derived. An application to bifurcating integer-valued autoregression is given. A Poisson bifurcating model is introduced.

Suggested Citation

  • Zhou, J. & Basawa, I.V., 2005. "Least-squares estimation for bifurcating autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 77-88, August.
    • Handle: RePEc:eee:stapro:v:74:y:2005:i:1:p:77-88
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    Citations

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    Cited by:

    1. 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.
    2. Hwang, S.Y. & Choi, M.S., 2009. "Modeling and large sample estimation for multi-casting autoregression," Statistics & Probability Letters, Elsevier, vol. 79(18), pages 1943-1950, September.
    3. 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.
    4. 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.
    5. Mao, Mingzhi, 2014. "The asymptotic behaviors for least square estimation of multi-casting autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 110-124.
    6. Zhang, Chenhua, 2011. "Parameter estimation for first-order bifurcating autoregressive processes with Weibull innovations," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1961-1969.
    7. Scotto, Manuel G. & Weiß, Christian H. & Silva, Maria Eduarda & Pereira, Isabel, 2014. "Bivariate binomial autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 233-251.
    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.

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