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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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File URL: http://halshs.archives-ouvertes.fr/docs/00/61/84/67/PDF/IF2011.pdf
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Bibliographic Info

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

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00618467/en/
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Related research

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. David I. Harvey & Stephen J. Leybourne, 2007. "Testing for time series linearity," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 149-165, 03.
  3. Wallis, Kenneth F., 2003. "Chi-squared tests of interval and density forecasts, and the Bank of England's fan charts," International Journal of Forecasting, Elsevier, vol. 19(2), pages 165-175.
  4. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2011. "Evaluating Value-at-Risk Models with Desk-Level Data," Management Science, INFORMS, vol. 57(12), pages 2213-2227, December.
  5. Candelon Bertrand & Colletaz Gilberg & Hurlin Christophe & Tokpavi Sessi, 2009. "Backtesting Value-at-Risk: A GMM Duration-based Test," Research Memorandum 051, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  6. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
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Cited by:
  1. Li, Yushu & Andersson, Jonas, 2014. "A Likelihood Ratio and Markov Chain Based Method to Evaluate Density Forecasting," Discussion Papers 2014/12, Department of Business and Management Science, Norwegian School of Economics.

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