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Limiting mixture distributions for AR(1) model indexed by a branching process

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  • Hwang, S.Y.
  • Baek, J.S.

Abstract

First order autoregressive model indexed by a supercritical Galton-Watson branching process is discussed. Limiting distributions of the least squares estimates are derived both for the stationary and explosive cases. It is shown that a certain random variable inherent in the branching process is acting as a mixing variable in limiting mixture distributions. In particular, with explosive Gaussian case, we obtain a mixture of Cauchy distributions rather than Cauchy.

Suggested Citation

  • Hwang, S.Y. & Baek, J.S., 2010. "Limiting mixture distributions for AR(1) model indexed by a branching process," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 2003-2008, December.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:2003-2008
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    References listed on IDEAS

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    1. 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.
    2. 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.
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