Backtesting Value-at-Risk Using Forecasts for Multiple Horizons, a Comment on the Forecast Rationality Tests of A.J. Patton and A. Timmermann
Lennart F. Hoogerheide
Vrije Universiteit Amsterdam - Dept. of Econometrics
Norges Bank; BI Norwegian Business School
H. K. van Dijk
Tinbergen Institute; Econometric Institute
September 20, 2011
Tinbergen Institute Discussion Paper 11-131/4
Patton and Timmermann (2011, 'Forecast Rationality Tests Based on Multi-Horizon Bounds', Journal of Business & Economic Statistics, forthcoming) propose a set of useful tests for forecast rationality or optimality under squared error loss, including an easily implemented test based on a regression that only involves (long-horizon and short-horizon) forecasts and no observations on the target variable. We propose an extension, a simulation-based procedure that takes into account the presence of errors in parameter estimates. This procedure can also be applied in the field of 'backtesting' models for Value-at-Risk. Applications to simple AR and ARCH time series models show that its power in detecting certain misspecifications is larger than the power of well-known tests for correct Unconditional Coverage and Conditional Coverage.
Number of Pages in PDF File: 17
Keywords: value-at-Risk, backtest, optimal revision, forecast rationality
JEL Classification: C12, C52, C53, C58, G32
Date posted: September 20, 2011
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