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Is a Normal Copula the Right Copula?

Author

Listed:
  • Dante Amengual
  • Enrique Sentana

Abstract

We derive computationally simple and intuitive expressions for score tests of Gaussian copulas against generalized hyperbolic alternatives, including symmetric and asymmetric Student t, and many other examples. We decompose our tests into third and fourth moment components, and obtain one-sided Likelihood Ratio analogs, whose standard asymptotic distribution we provide. Our Monte Carlo exercises confirm the reliable size of parametric bootstrap versions of our tests, and their substantial power gains over alternative procedures. In an empirical application to CRSP stocks, we find that short-term reversals and momentum effects are better captured by non-Gaussian copulas, whose parameters we estimate by indirect inference. Supplementary materials for this article are available online.

Suggested Citation

  • Dante Amengual & Enrique Sentana, 2020. "Is a Normal Copula the Right Copula?," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 350-366, April.
    • Handle: RePEc:taf:jnlbes:v:38:y:2020:i:2:p:350-366
    DOI: 10.1080/07350015.2018.1505631
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    Cited by:

    1. Liang Chen & Juan J. Dolado & Jesús Gonzalo, 2021. "Quantile Factor Models," Econometrica, Econometric Society, vol. 89(2), pages 875-910, March.
    2. Fiorentini, Gabriele & Sentana, Enrique, 2021. "New testing approaches for mean–variance predictability," Journal of Econometrics, Elsevier, vol. 222(1), pages 516-538.
    3. Amengual, Dante & Fiorentini, Gabriele & Sentana, Enrique, 2024. "Specification tests for non-Gaussian structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 244(2).
    4. Shiraya, Kenichiro & Yamakami, Tomohisa, 2024. "Constructing copulas using corrected Hermite polynomial expansion for estimating cross foreign exchange volatility," European Journal of Operational Research, Elsevier, vol. 314(3), pages 1195-1214.
    5. Oh, Dong Hwan & Patton, Andrew J., 2023. "Dynamic factor copula models with estimated cluster assignments," Journal of Econometrics, Elsevier, vol. 237(2).
    6. Sentana, Enrique & Amengual, Dante & Bei, Xinyue, 2020. "Hypothesis tests with a repeatedly singular information matrix," CEPR Discussion Papers 14415, C.E.P.R. Discussion Papers.
    7. Woźny, Jakub & Jaworski, Piotr & Jelito, Damian & Pitera, Marcin & Wyłomańska, Agnieszka, 2025. "Gaussian dependence structure pairwise goodness-of-fit testing based on conditional covariance and the 20/60/20 rule," Journal of Multivariate Analysis, Elsevier, vol. 206(C).

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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