The smooth transition GARCH model: application to international stock indexes

The aim of this article is to study the dynamics of four international stock indexes, by developing a model that introduces asymmetry and nonlinearity on the conditional variance. The Smooth Transition Generalized Autoregressive Conditional Heteroscedastic (STGARCH) model is considered, where the possibility of intermediate regimes is modelled with the introduction of a smooth transition mechanism in a Generalized Autoregressive Conditional Heteroscedastic (GARCH) specification. The transition function is either logistic (the Logistic Smooth Transition GARCH (LSTGARCH) model) or exponential (the Exponential Smooth Transition GARCH (EST-GARCH) model). It is found that, on one side, an important characteristic of the LSTGARCH model is that it highlights the asymmetric effect of unanticipated shocks on the conditional volatility. On the other side, the ESTGARCH model allows the dynamics of the conditional variance to be independent of the sign of past news. Indeed, this model allows to highlight the size effect of the shocks, so that small and big shocks have separate effects. I find that this model performs better than the symmetric GARCH model by allowing for asymmetry and regime changes on the conditional volatility and for gradual change on the transition parameter.