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Limiting mixture distributions for AR(1) model indexed by a branching process
- Authors
- Hwang, S. Y.; Baek, J. S.
- Issue Date
- 1-Dec-2010
- Publisher
- ELSEVIER SCIENCE BV
- Keywords
- AR(1); Branching process; Cauchy mixture; Limiting mixture distribution
- Citation
- STATISTICS & PROBABILITY LETTERS, v.80, no.23-24, pp 2003 - 2008
- Pages
- 6
- Journal Title
- STATISTICS & PROBABILITY LETTERS
- Volume
- 80
- Number
- 23-24
- Start Page
- 2003
- End Page
- 2008
- ISSN
- 0167-7152
1879-2103
- 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. (C) 2010 Elsevier B.V. All rights reserved.
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