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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

Author

Listed:
  • Lennart F. Hoogerheide

    (VU University Amsterdam)

  • Francesco Ravazzolo

    (Norges Bank)

  • Herman K. van Dijk

    (Erasmus University Rotterdam, VU University Amsterdam.)

Abstract

Patton and Timmermann (2011, “Forecast Rationality Tests Based on Multi-Horizon Bounds”, Journal of Business & Economic Statistics , 30(1), 1-17) 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.

Suggested Citation

  • Lennart F. Hoogerheide & Francesco Ravazzolo & Herman K. van Dijk, 2011. "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 Papers 11-131/4, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20110131
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    References listed on IDEAS

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    1. Andrew Patton & Allan Timmermann, 2012. "Forecast Rationality Tests Based on Multi-Horizon Bounds," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 1-17.
    2. Hoogerheide, Lennart & van Dijk, Herman K., 2010. "Bayesian forecasting of Value at Risk and Expected Shortfall using adaptive importance sampling," International Journal of Forecasting, Elsevier, vol. 26(2), pages 231-247, April.
    3. Hoogerheide, Lennart F. & Kaashoek, Johan F. & van Dijk, Herman K., 2007. "On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: An application of flexible sampling methods using neural networks," Journal of Econometrics, Elsevier, vol. 139(1), pages 154-180, July.
    4. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Boucher, Christophe M. & Daníelsson, Jón & Kouontchou, Patrick S. & Maillet, Bertrand B., 2014. "Risk models-at-risk," Journal of Banking & Finance, Elsevier, vol. 44(C), pages 72-92.
    2. Billio, Monica & Casarin, Roberto & Ravazzolo, Francesco & van Dijk, Herman K., 2013. "Time-varying combinations of predictive densities using nonlinear filtering," Journal of Econometrics, Elsevier, vol. 177(2), pages 213-232.

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    More about this item

    Keywords

    Value-at-Risk; backtest; optimal revision; forecast rationality;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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