Bayesian estimation of smooth transition GARCH model using Gibbs sampling

Research into time series models of changing variance and covariance, which is often called volatility model, has exploded in the last 10 years. Financial series are characterized by periods of large volatility followed by periods of relative quietness. This type of clustering led to the idea that volatility is predictable. The ARCH and GARCH models were quite successful in predicting volatility compared to more traditional methods. But better predictions are obtained when asymmetries and nonlinearities in the response of volatility to news arriving in the market are taken into account. In this paper we propose a new kind of asymmetric GARCH in which the conditional variance obeys two different regimes with a smooth transition function. In this model, the conditional variance reacts differently to negative and positive shocks and its magnitude on shocks have separate effects. As financial data have very often a high frequency of observation, smooth transition seems a priori better than an abrupt transition. The change of regime occurs when the residuals cross the threshold zero. This threshold GARCH models can be generalized using a smooth transition function FT(η,st) taking continuous values between zero and one. We treat the joint point t* and the speed of adjustment η to be two unknown parameters.