The threshold GARCH model: estimation and density forecasting for financial returns

This paper develops a novel density forecasting method for financial time series following a threshold GARCH model that does not require the estimation of the model itself. Instead, Bayesian inference is performed about an induced multiple threshold one-step ahead value-at-risk process at a single quantile level. This is achieved by a quasi-likelihood approach that uses quantile information. We describe simulation studies that provide insight into our method and illustrate it using empirical work on market returns. The results show that our forecasting method outperforms some benchmark models for density forecasting of financial returns.