  This work investigates the effects of using the independent Jeffreys prior
for the degrees of freedom parameter of a Student-t model in the asymmetric
generalised autoregressive conditional heteroskedasticity (GARCH) model. To
capture asymmetry in the reaction to past shocks, smooth transition models are
assumed for the variance. We adopt the fully Bayesian approach for inference,
prediction and model selection We discuss problems related to the estimation of
degrees of freedom in the Student-t model and propose a solution based on
independent Jeffreys priors which correct problems in the likelihood function.
A simulated study is presented to investigate how the estimation of model
parameters in the Student-t GARCH model are affected by small sample sizes,
prior distributions and misspecification regarding the sampling distribution.
An application to the Dow Jones stock market data illustrates the usefulness of
the asymmetric GARCH model with Student-t errors.
