A novel approach to modelling the distribution of financial returns

We develop a novel quantile function threshold GARCH model for studying the distribution function, rather than the volatility function, of financial returns that follow a threshold GARCH model. We propose a Bayesian method to do estimation and forecasting simultaneously, which allows us to handle multiple thresholds easily and ensures the forecasts can take account of the variation of model parameters. We apply the method to simulated data and Nasdaq returns. We show that our model is robust to model specification errors and outperforms some commonly used threshold GARCH models.