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Skew-Normal Mixture and Markov-Switching GARCH Processes

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  • Haas Markus

    (University of Munich)

Abstract

This paper introduces skew-normal (SN) mixture and Markov-switching (MS) GARCH processes for capturing the skewness in the distribution of stock returns. The model class is motivated by the fact that the common way of incorporating asymmetries into Gaussian MS GARCH models, i.e., regime-dependent means, leads to autocorrelated raw returns, which may not be desirable. The appearance of the SN distribution can be explained by a pre-asymptotic behavior of daily stock returns, and can still be viewed as "generic." The dynamic properties of the process are derived, and its in- and out-of-sample performance is compared with that of several competing models in an application to three major European stock markets over a period covering the recent financial turmoil. It turns out that parsimoniously parameterized SN mixture GARCH processes perform best overall. In particular, they outperform both a skewed t GARCH specification as well as normal mixture GARCH models with skewness generated via nonzero component means.

Suggested Citation

  • Haas Markus, 2010. "Skew-Normal Mixture and Markov-Switching GARCH Processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-56, September.
    • Handle: RePEc:bpj:sndecm:v:14:y:2010:i:4:n:1
    DOI: 10.2202/1558-3708.1765
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    3. Bernardi, Mauro, 2013. "Risk measures for skew normal mixtures," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1819-1824.
    4. Augustyniak, Maciej, 2014. "Maximum likelihood estimation of the Markov-switching GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 61-75.
    5. AUGUSTYNIAK, Maciej & BAUWENS, Luc & DUFAYS, Arnaud, 2016. "A New Approach to Volatility Modeling : The High-Dimensional Markov Model," LIDAM Discussion Papers CORE 2016042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Maciej Augustyniak & Frédéric Godin & Clarence Simard, 2017. "Assessing the effectiveness of local and global quadratic hedging under GARCH models," Quantitative Finance, Taylor & Francis Journals, vol. 17(9), pages 1305-1318, September.
    7. Broda, Simon A. & Krause, Jochen & Paolella, Marc S., 2018. "Approximating expected shortfall for heavy-tailed distributions," Econometrics and Statistics, Elsevier, vol. 8(C), pages 184-203.
    8. Markus Haas, 2012. "A Note on the Moments of the Skew-Normal Distribution," Economics Bulletin, AccessEcon, vol. 32(4), pages 3306-3312.

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