Likelihood-based scoring rules for comparing density forecasts in tails

We propose 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. These scoring rules can be interpreted in terms of Kullback–Leibler d...

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Bibliographic Details
Published in:Econometrics 2011-08, Vol.163 (2), p.215-230
Main Authors: Diks, Cees, Panchenko, Valentyn, van Dijk, Dick
Format: Article
Language:English
Subjects:
Applications
Censored likelihood
Comparative analysis
Conditional likelihood
Decision theory
Density forecast evaluation
Density forecast evaluation Scoring rules Weighted likelihood ratio scores Conditional likelihood Censored likelihood Risk management
Econometrics
Economic theory
Exact sciences and technology
Forecasting techniques
Forecasts
Insurance, economics, finance
Mathematics
Maximum likelihood method
Nonparametric inference
Probability
Probability and statistics
Probability distribution
Quantitative Finance
Risk management
Sciences and techniques of general use
Scoring rules
Statistical Finance
Statistics
Studies
Weighted likelihood ratio scores
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Summary:We propose 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. These scoring rules can be interpreted in terms of Kullback–Leibler divergence between weighted versions of the density forecast and the true density. Existing scoring rules based on weighted likelihood favor density forecasts with more probability mass in the given region, rendering predictive accuracy tests biased toward such densities. Using our novel likelihood-based scoring rules avoids this problem.
ISSN:0304-4076
2225-1146
1872-6895
2225-1146
DOI:10.1016/j.jeconom.2011.04.001