Stock Index Returns' Density Prediction using GARCH Models: Frequentist or Bayesian Estimation?

Using well-known GARCH models for density prediction of daily S&P 500 and Nikkei 225 index returns, a comparison is provided between frequentist and Bayesian estimation. No significant difference is found between the qualities of the forecasts of the whole density, whereas the Bayesian approach exhibits significantly better left-tail forecast accuracy