Backtesting Value-at-Risk and Expected Shortfall in the Presence of Estimation Error

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Tinbergen Institute Discussion Paper ; No. TI 2019-059/III

Classification and Topics

• Classification: Wirtschaft ; Hypothesis Testing: General ; Forecasting Models; Simulation Methods ; Financial Econometrics ; Financial Forecasting and Simulation
• Subject: expected shortfall ; backtesting ; risk management ; tail risk ; Value-at-Risk

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Barendse, Sander ; Kole, Erik ; van Dijk, Dick
• Event: Veröffentlichung
• (who): Tinbergen Institute
• (where): Amsterdam and Rotterdam
• (when): 2019

Further information

• Handle: http://hdl.handle.net/10419/205348
• Last update: 10.03.2025, 11:43 AM CET