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Testing Interval Forecasts: A GMM‐Based Approach

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  • Elena‐Ivona Dumitrescu
  • Christophe Hurlin
  • Jaouad Madkour

Abstract

This paper proposes a new evaluation framework for interval forecasts. Our model-free test can be used to evaluate interval forecasts and high-density regions, potentially discontinuous and/or asymmetric. Using a simple J-statistic, based on the moments defined 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 confirms 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," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(2), pages 97-110, March.
    • Handle: RePEc:wly:jforec:v:32:y:2013:i:2:p:97-110
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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, Oxford University Press, vol. 9(2), pages 314-343, Spring.
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    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, March.
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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, Norwegian School of Economics, Department of Business and Management Science.
    2. 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.

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