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

作者：Hwang S Y^*; Baek J S

来源：Statistics & Probability Letters, 2010, 80(23-24): 2003-2008.

DOI：10.1016/j.spl.2010.09.006

• AR(1)
• Branching process
• Cauchy mixture
• Limiting mixture distribution

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.

• 出版日期2010-12-1