Hidden Markov models with t components. Increased persistence and other aspects

Abstract

Hidden Markov models have been applied in many different fields, including econometrics and finance. However, the lion's share of the investigated models concerns Markovian mixtures of Gaussian distributions. We present an extension to conditional t-distributions, including models with unequal distribution types in different states. It is shown that the extended models, on the one hand, reproduce various stylized facts of daily returns better than the common Gaussian model. On the other hand, robustness to outliers and persistence of the visited states increases significantly.

Keywords:

• Hidden Markov model
• Markov-switching model
• State persistence
• t-distribution
• Daily returns

Acknowledgements

We would like to thank Professors H. Hering, T. Teräsvirta, P. Thomson, D. Vere-Jones and W. Zucchini for their inspiring comments and support. We would also like to thank the participants of the Cherry Bud Workshop 2007 and the 17th NZESG for helpful feedback. We thank two anonymous referees whose comments led to major improvements of the paper as well as Drs I. Bulla, S. Mergner, and K. Thangavelu for editorial assistance. Not to forget, we thank G. Allardice, W. Allardice, and Prof. D. Vere-Jones for the great working environment. The work of Jan Bulla was supported, in part, by a fellowship within the Postdoc Programme of the German Research Foundation (DFG).