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
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: Suggested Citation