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Biometrika 2009 96(3):751-760; doi:10.1093/biomet/asp031
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© 2009 Biometrika Trust

Article

A Student t-mixture autoregressive model with applications to heavy-tailed financial data

C. S. Wong and W. S. Chan

Department of Finance, The Chinese University of Hong Kong, Shatin, Hong Kong albertw{at}baf.msmail.cuhk.edu.hk chanws{at}cuhk.edu.hk

P. L. Kam

Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong h102934{at}graduate.hku.hk

Received for publication 1 December 2007. Revision received 1 November 2008.
  Abstract

We introduce the class of Student t-mixture autoregressive models, which is promising for financial time series modelling. The model is able to capture serial correlations, time-varying means and volatilities, and the shape of the conditional distributions can be time varied from short-tailed to long-tailed, or from unimodal to multimodal. The use of t-distributed errors in each component of the model allows conditional leptokurtic distributions that account for the commonly observed excess unconditional kurtosis in financial data. Methods of parameter estimation and model selection are given. Finally, the proposed modelling procedure is illustrated through a real example.

Key Words: EM algorithm • Interest rate • Mixture distribution • Nonlinear time series model • Student t-distribution


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