Smooth Transition Garch Models : A

This paper proposes a new kind of asymmetric GARCH where the conditional variance obeys two diierent regimes with a smooth transition function. In one formulation, the conditional variance reacts diierently to negative and positive shocks while in a second formulation, small and big shocks have separate eeects. The introduction of a threshold allows for a mixed eeect. 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. The basic idea of this paper (smooth transition GARCH) grew out during the visit of Timo Terasvirta at GREQAM in September 1996. Once a rst version of this paper was completed and presented at EC 2 , Florence December 1996, it appeared that a similar eeort has been pursued in a classical framework by Gonzales-Riviera (1996) and by by Hagerud (1997). Some of the ideas concerning the reparameterisation of GARCH models have been explored in discussions with Rob Engle during his visit in Marseille in June 1992, conversations later pursued with Jean-Frann cois Richard. Many discussions and critics with Luc Bauwens helped a lot in the writing of the paper. Usual disclaimers apply. Support of the European Commission Human Capital and Mobility Program through the network \Econometric inference using simulation methods" is gratefully acknowledged.