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Journal of Probability and Statistics
Volume 2012 (2012), Article ID 167431, 16 pages
http://dx.doi.org/10.1155/2012/167431
Research Article

Bayesian Non-Parametric Mixtures of GARCH(1,1) Models

School of Mathematics and Statistics, The University of Western Australia, Perth, Australia

Received 2 March 2012; Revised 16 May 2012; Accepted 18 May 2012

Academic Editor: Ori Rosen

Copyright © 2012 John W. Lau and Ed Cripps. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Traditional GARCH models describe volatility levels that evolve smoothly over time, generated by a single GARCH regime. However, nonstationary time series data may exhibit abrupt changes in volatility, suggesting changes in the underlying GARCH regimes. Further, the number and times of regime changes are not always obvious. This article outlines a nonparametric mixture of GARCH models that is able to estimate the number and time of volatility regime changes by mixing over the Poisson-Kingman process. The process is a generalisation of the Dirichlet process typically used in nonparametric models for time-dependent data provides a richer clustering structure, and its application to time series data is novel. Inference is Bayesian, and a Markov chain Monte Carlo algorithm to explore the posterior distribution is described. The methodology is illustrated on the Standard and Poor's 500 financial index.