Combining density forecasts using focused scoring rules

Anne Opschoor*, Dick Van Dijk, Michel van der Wel

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

We investigate the added value of combining density forecasts focused on a specific region of support. We develop forecast combination schemes that assign weights to individual predictive densities based on the censored likelihood scoring rule and the continuous ranked probability scoring rule (CRPS) and compare these to weighting schemes based on the log score and the equally weighted scheme. We apply this approach in the context of measuring downside risk in equity markets using recently developed volatility models, including HEAVY, realized GARCH and GAS models, applied to daily returns on the S&P 500, DJIA, FTSE and Nikkei indexes from 2000 until 2013. The results show that combined density forecasts based on optimizing the censored likelihood scoring rule significantly outperform pooling based on equal weights, optimizing the CRPS or log scoring rule. In addition, 99% Value-at-Risk estimates improve when weights are based on the censored likelihood scoring rule.

Original languageEnglish
Pages (from-to)1298-1313
Number of pages16
JournalJournal of Applied Econometrics
Volume32
Issue number7
DOIs
Publication statusPublished - 2017

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