A quantile function approach to the distribution of financial returns following TGARCH models

Abstract

We develop a novel quantile function approach to the distribution of financial returns that follow threshold GARCH models. We propose a Bayesian method to do estimation and forecasting simultaneously, which ensures that the density forecasts can take account of the variation of model parameters. This method also allows us to handle multiple thresholds easily. We conduct extensive simulation studies and apply our method to Nasdaq returns. The results show that our approach is robust to model specification errors and outperforms some commonly used benchmark models.