  The main goal of this paper is an application of Bayesian model comparison,
based on the posterior probabilities and posterior odds ratios, in testing the
explanatory power of the set of competing GARCH (ang. Generalised
Autoregressive Conditionally Heteroscedastic) specifications, all with
asymmetric and heavy tailed conditional distributions. In building competing
volatility models we consider, as an initial specification, GARCH process with
conditional Student-t distribution with unknown degrees of freedom parameter,
proposed by Bollerslev (1987). By introducing skewness into Student-t family
and incorporating the resulting class as a conditional distribution we
generated various GARCH models, which compete in explaining possible asymmetry
of both conditional and unconditional distribution of financial data. Based on
the daily returns of hypothetical financial time series, we discuss the results
of Bayesian comparison of alternative skewing mechanisms applied in the initial
Student-t GARCH framework. We also check the sensitivity of model ranking with
respect to the changes in prior distribution of model specific parameters.
Additionally, we present formal Bayesian inference about conditional asymmetry
of the distribution of the daily returns in all competing specifications on the
basis of the skewness measure defined by Arnold and Groenveld (1995).
