Contents

Improving Value-at-Risk estimates by combining density forecasts 1 This research focuses on the properties of weighted linear combinations of pre-diction models, evaluated using log predictive scoring rule and new scoring rules based on conditional and censored likelihood for assessing the predictive accuracy of competing density forecasts over a specific region of interest, such as the left tail in financial risk management. We apply the technique above on 20 prediction models for forecasting the daily S&P 500 returns and analyze this framework both ex post and ex ante. We find that the VaR and ES estimates are more accurate through combining density forecasts using the conditional and censored likelihood scoring rules than the log predictive scoring rule