Combining Density Forecasts using Focused Scoring Rules

Tinbergen Institute Discussion Paper 14-090/III

35 Pages Posted: 22 Jul 2014 Last revised: 14 Jan 2017

See all articles by Anne Opschoor

Anne Opschoor

Vrije Universiteit Amsterdam

Dick J. C. van Dijk

Erasmus University Rotterdam - Erasmus School of Economics - Econometric Institute; ERIM

Michel van der Wel

Erasmus University Rotterdam

Date Written: December 23, 2016

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&P500, 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% VaR estimates improve when weights are based on the censored likelihood scoring rule.

Keywords: Density forecast evaluation, Volatility modeling, Censored likelihood, Value-at-Risk

JEL Classification: C53, C58, G17

Suggested Citation

Opschoor, Anne and van Dijk, Dick J.C. and van der Wel, Michel, Combining Density Forecasts using Focused Scoring Rules (December 23, 2016). Tinbergen Institute Discussion Paper 14-090/III, Available at SSRN: https://ssrn.com/abstract=2469024 or http://dx.doi.org/10.2139/ssrn.2469024

Anne Opschoor (Contact Author)

Vrije Universiteit Amsterdam ( email )

De Boelelaan 1105
Amsterdam, NL 1081 HV
Netherlands

Dick J.C. Van Dijk

Erasmus University Rotterdam - Erasmus School of Economics - Econometric Institute

P.O. Box 1738
3000 DR Rotterdam
Netherlands

ERIM ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 10 408 1263 (Phone)
+31 10 4089162 (Fax)

HOME PAGE: http://people.few.eur.nl/djvandijk

Michel Van der Wel

Erasmus University Rotterdam ( email )

Burg. Oudlaan 50
Rotterdam, NL 3062 PA
Netherlands

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