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Testing interval forecasts: a GMM-based approach

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Author Info

  • Elena-Ivona Dumitrescu

    () (LEO - Laboratoire d'économie d'Orleans - CNRS : UMR6221 - Université d'Orléans)

  • Christophe Hurlin

    () (LEO - Laboratoire d'économie d'Orleans - CNRS : UMR6221 - Université d'Orléans)

  • Jaouad Madkour

    (LEO - Laboratoire d'économie d'Orleans - CNRS : UMR6221 - Université d'Orléans)

Abstract

This paper proposes a new evaluation framework for interval forecasts. Our model free test can be used to evaluate intervals forecasts and High Density Regions, potentially discontinuous and/or asymmetric. Using a simple J-statistic, based on the moments de ned by the orthonormal polynomials associated with the Binomial distribution, this new approach presents many advantages. First, its implementation is extremely easy. Second, it allows for a separate test for unconditional coverage, independence and conditional coverage hypotheses. Third, Monte-Carlo simulations show that for realistic sample sizes, our GMM test has good small-sample properties. These results are corroborated by an empirical application on SP500 and Nikkei stock market indexes. It con rms that using this GMM test leads to major consequences for the ex-post evaluation of interval forecasts produced by linear versus nonlinear models.

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Paper provided by HAL in its series Working Papers with number halshs-00618467.

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Date of creation: Aug 2011
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Handle: RePEc:hal:wpaper:halshs-00618467

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Keywords: Interval forecasts; High Density Region; GMM.;

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  1. Bontemps, Christian & Meddahi, Nour, 2005. "Testing normality: a GMM approach," Journal of Econometrics, Elsevier, vol. 124(1), pages 149-186, January.
  2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  3. David I. Harvey & Stephen J. Leybourne, 2007. "Testing for time series linearity," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 149-165, 03.
  4. Peter Christoffersen & Jeremy Berkowitz & Denis Pelletier, 2008. "Evaluating Value-at-Risk Models with Desk-Level Data," CREATES Research Papers 2009-35, School of Economics and Management, University of Aarhus.
  5. Wallis, Kenneth F., 2002. "Chi-squared tests of interval and density forecasts, and the Bank of England's fan charts," Royal Economic Society Annual Conference 2002 181, Royal Economic Society.
  6. Bertrand Candelon & Gilbert Colletaz & Christophe Hurlin & Sessi Tokpavi, 2011. "Backtesting Value-at-Risk: A GMM Duration-Based Test," Journal of Financial Econometrics, Oxford University Press, vol. 9(2), pages 314-343, Spring.
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