Likelihood-based scoring rules for comparing density forecasts in tails

摘要: Abstract We propose new scoring rules based on conditional and censored likelihood for assessing the predictive accuracy of competing density forecasts over a specific region interest, such as left tail in financial risk management. These can be interpreted terms Kullback–Leibler divergence between weighted versions forecast true density. Existing favor with more probability mass given region, rendering tests biased toward densities. Using our novel likelihood-based avoids this problem.