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Testing interval forecasts: a GMM-based approach

  • 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)

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
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00618467/en/
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  1. Christophe Hurlin & Gilbert Colletaz & Sessi Tokpavi & Bertrand Candelon, 2008. "Backtesting Value-at-Risk: A GMM Duration-Based Test," Working Papers halshs-00329495, HAL.
  2. Bertrand Candelon & Gilbert Colletaz & Christophe Hurlin & Sessi Tokpavi, 2011. "Backtesting Value-at-Risk: A GMM Duration-Based Test," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(2), pages 314-343, Spring.
  3. BONTEMPS, Christian & MEDDAHI, Nour, 2002. "Testing Normality : A GMM Approach," Cahiers de recherche 2002-14, Universite de Montreal, Departement de sciences economiques.
  4. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  5. Wallis, Kenneth F., 2001. "Chi-squared tests of interval and density forecasts and the Bank of England's fan charts," Working Paper Series 0083, European Central Bank.
  6. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2005. "Evaluating Value-at-Risk models with desk-level data," Working Paper Series 010, North Carolina State University, Department of Economics, revised Dec 2006.
  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.
  8. 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.
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