Skew-Normal Mixture and Markov-Switching GARCH Processes

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.