Backtesting Value-at-Risk and Expected Shortfall in the Presence of Estimation Error
نویسندگان
چکیده
Abstract We investigate the effect of estimation error on backtests expected shortfall (ES) forecasts. These are based first-order conditions a recently introduced family jointly consistent loss functions for value-at-risk (VaR) and ES. For both single multiperiod horizons, we provide explicit expressions additional terms in asymptotic covariance matrix that result from error, propose robust tests account it. Monte Carlo experiments show ignore these suffer size distortions, which more pronounced higher ratios out-of-sample to in-sample observations. Robust versions perform well with power against common alternatives. also introduce novel standardization conditional joint test statistic removes need estimate higher-order moments significantly improves its performance. In an application VaR ES forecasts daily FTSE 100 index returns as generated by (GJR-)GARCH HEAVY models, find substantially impacts outcome backtests, is not bound particular subperiods such credit crisis.
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ژورنال
عنوان ژورنال: Journal of Financial Econometrics
سال: 2021
ISSN: ['1479-8409', '1479-8417']
DOI: https://doi.org/10.1093/jjfinec/nbab008