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Testing Interval Forecasts: a GMM-Based Approach

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  • Elena Ivona Dumitrescu

    () (EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

  • Christophe Hurlin
  • Jaouad Madkour

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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Suggested Citation

  • Elena Ivona Dumitrescu & Christophe Hurlin & Jaouad Madkour, 2013. "Testing Interval Forecasts: a GMM-Based Approach," Post-Print hal-01385898, HAL.
  • Handle: RePEc:hal:journl:hal-01385898
    Note: View the original document on HAL open archive server: https://hal-univ-paris10.archives-ouvertes.fr/hal-01385898
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    References listed on IDEAS

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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.
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    3. 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.
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    6. 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.
    7. 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.
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    1. Weron, Rafał, 2014. "Electricity price forecasting: A review of the state-of-the-art with a look into the future," International Journal of Forecasting, Elsevier, vol. 30(4), pages 1030-1081.
    2. Li, Yushu & Andersson, Jonas, 2014. "A Likelihood Ratio and Markov Chain Based Method to Evaluate Density Forecasting," Discussion Papers 2014/12, Norwegian School of Economics, Department of Business and Management Science.

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