Smooth transition GARCH models: a Bayesian perspective

This paper proposes a new kind of asymmetric GARCH where the conditional variance obeys two different regimes with a smooth transition function. In one formulation, the conditional variance reacts differently to negative and positive shocks while in a second formulation, small and big shocks have separate effects. The introduction of a threshold allows for a mixed effect. A Bayesian strategy, based on the comparison between posterior and predictive Bayesian residuals, is built for detecting the presence and the shape of nonlinearities. The method is applied to the Brussels and Tokyo stock indexes. The need for an alternative parameterisation of the GARCH model is emphasised as a solution to numerical problems.