Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/205348 
Year of Publication: 
2019
Series/Report no.: 
Tinbergen Institute Discussion Paper No. TI 2019-059/III
Publisher: 
Tinbergen Institute, Amsterdam and Rotterdam
Abstract: 
We investigate the effect of estimation error on backtests of (multi-period) expected shortfall (ES) forecasts. These backtests are based on first order conditions of a recently introduced family of jointly consistent loss functions for Value-at-Risk (VaR) and ES. We provide explicit expressions for the additional terms in the asymptotic covariance matrix that result from estimation error, and propose robust tests that account for it. Monte Carlo experiments show that the tests that ignore these terms suffer from size distortions, which are more pronounced for higher ratios of out-of-sample to in-sample observations. Robust versions of the backtests perform well, although this also depends on the choice of conditioning variables. In an application to VaR and ES forecasts for daily FTSE 100 index returns as generated by AR-GARCH, AR-GJR-GARCH, and AR-HEAVY models, we find that estimation error substantially impacts the outcome of the backtests.
Subjects: 
expected shortfall
backtesting
risk management
tail risk
Value-at-Risk
JEL: 
C12
C53
C58
G17
Document Type: 
Working Paper

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