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Testing Distributional Assumptions: A GMM Approach

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  • N. MEDDAHI
  • C. BONTEMPS

Abstract

In this paper, we consider testing marginal distributional assumptions. Special cases that we consider are the Pearson's family like the Gaussian, Student, Gamma, Beta and uniform distributions. The test statistics we consider are based on the first moment conditions derived by Hansen and Scheinkman (1995) when one considers a continuous time model. These moment conditions are valid even if the observations are not a sample of a continuous time model. We treat in detail the parameter uncertainty problem when the considered process is not observed but depends on estimators of unknown parameters. We also consider the time series case and adopt a HAC approach for this purpose. This is a generalization of Bontemps and Meddahi (2002) who considered this approach for the Normal case

Suggested Citation

  • N. Meddahi & C. Bontemps, 2004. "Testing Distributional Assumptions: A GMM Approach," Econometric Society 2004 North American Winter Meetings 487, Econometric Society.
    • Handle: RePEc:ecm:nawm04:487
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    10. Corradi, Valentina & Swanson, Norman R., 2006. "Predictive density and conditional confidence interval accuracy tests," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 187-228.
    11. Ames, Matthew & Bagnarosa, Guillaume & Peters, Gareth W., 2017. "Violations of uncovered interest rate parity and international exchange rate dependences," Journal of International Money and Finance, Elsevier, vol. 73(PA), pages 162-187.
    12. Sullivan Hu'e & Christophe Hurlin & Yang Lu, 2024. "Backtesting Expected Shortfall: Accounting for both duration and severity with bivariate orthogonal polynomials," Papers 2405.02012, arXiv.org, revised May 2024.
    13. Denisa Georgiana Banulescu & Gilbert Colletaz & Christophe Hurlin & Sessi Tokpavi, 2013. "High-Frequency Risk Measures," Working Papers halshs-00859456, HAL.
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    15. Rodríguez, Gabriel, 2017. "Modeling Latin-American stock and Forex markets volatility: Empirical application of a model with random level shifts and genuine long memory," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 393-420.
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    17. Malte Knüppel, 2015. "Evaluating the Calibration of Multi-Step-Ahead Density Forecasts Using Raw Moments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 270-281, April.
    18. Ryan Janicki & Tucker S. McElroy, 2016. "Hermite expansion and estimation of monotonic transformations of Gaussian data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 207-234, March.
    19. Wang, Keli & Liu, Xiaoquan & Ye, Wuyi, 2023. "Intraday VaR: A copula-based approach," Journal of Empirical Finance, Elsevier, vol. 74(C).
    20. Amengual, Dante & Fiorentini, Gabriele & Sentana, Enrique, 2013. "Sequential estimation of shape parameters in multivariate dynamic models," Journal of Econometrics, Elsevier, vol. 177(2), pages 233-249.
    21. Amengual, Dante & Carrasco, Marine & Sentana, Enrique, 2020. "Testing distributional assumptions using a continuum of moments," Journal of Econometrics, Elsevier, vol. 218(2), pages 655-689.
    22. Slim, Skander & Koubaa, Yosra & BenSaïda, Ahmed, 2017. "Value-at-Risk under Lévy GARCH models: Evidence from global stock markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 46(C), pages 30-53.
    23. Patrick Marsh, 2019. "Nonparametric conditional density specification testing and quantile estimation; with application to S&P500 returns," Discussion Papers 19/02, University of Nottingham, Granger Centre for Time Series Econometrics.

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    More about this item

    Keywords

    GMM; Hansen-Scheinkman moment conditions; parameter uncertainty; serial correlation;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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