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Testing interval forecasts: a GMM-based approach

Author Info

  • Elena-Ivona Dumitrescu

    ()

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

  • Christophe Hurlin

    ()

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

  • Jaouad Madkour

    (LEO - Laboratoire d'économie d'Orleans - CNRS - UO - 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: https://halshs.archives-ouvertes.fr/halshs-00618467/document
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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
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00618467
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Keywords: GMM; Interval forecasts; High Density Region; GMM.;

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  1. 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.
  2. Christian BONTEMPS & Nour MEDDAHI, 2002. "Testing Normality : A Gmm Approach," Cahiers de recherche 14-2002, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Peter Christoffersen & Jeremy Berkowitz & Denis Pelletier, 2008. "Evaluating Value-at-Risk Models with Desk-Level Data," CREATES Research Papers 2009-35, Department of Economics and Business Economics, Aarhus University.
  4. Gilbert Colletaz & Christophe Hurlin & Sessi Tokpavi, 2008. "Backtesting Value-at-Risk : A GMM Duration-based Test," Post-Print halshs-00363165, HAL.
  5. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  6. Michael P. Clements & Nick Taylor, 2003. "Evaluating interval forecasts of high-frequency financial data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(4), pages 445-456.
  7. David I. Harvey & Stephen J. Leybourne, 2007. "Testing for time series linearity," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 149-165, 03.
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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.
  2. Rafal Weron, 2014. "Electricity price forecasting: A review of the state-of-the-art with a look into the future," HSC Research Reports HSC/14/07, Hugo Steinhaus Center, Wroclaw University of Technology.

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