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Backtesting Value-at-Risk Using Forecasts for Multiple Horizons, a Comment on the Forecast Rationality Tests of A.J. Patton and A. Timmermann

Tinbergen Institute Discussion Paper 11-131/4

17 Pages Posted: 20 Sep 2011  

Lennart F. Hoogerheide

Vrije Universiteit Amsterdam - Dept. of Econometrics

Francesco Ravazzolo

Free University of Bolzano

H. K. van Dijk

Tinbergen Institute; Econometric Institute

Date Written: September 20, 2011

Abstract

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.

Keywords: value-at-Risk, backtest, optimal revision, forecast rationality

JEL Classification: C12, C52, C53, C58, G32

Suggested Citation

Hoogerheide, Lennart F. and Ravazzolo, Francesco and van Dijk, H. K., Backtesting Value-at-Risk Using Forecasts for Multiple Horizons, a Comment on the Forecast Rationality Tests of A.J. Patton and A. Timmermann (September 20, 2011). Tinbergen Institute Discussion Paper 11-131/4. Available at SSRN: https://ssrn.com/abstract=1930841 or http://dx.doi.org/10.2139/ssrn.1930841

Lennart F. Hoogerheide (Contact Author)

Vrije Universiteit Amsterdam - Dept. of Econometrics ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Francesco Ravazzolo

Free University of Bolzano ( email )

Bolzano
Italy

Herman K. Van Dijk

Econometric Institute ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 10 4088955 (Phone)
+31 10 4527746 (Fax)

Tinbergen Institute ( email )

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