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Is a Normal Copula the Right Copula?

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Abstract

We derive computationally simple and intuitive expressions for score tests of Gaussian copulas against Generalised Hyperbolic alternatives, including symmetric and asymmetric Student t, and Hermite polynomial expansions. We decompose our tests into third and fourth moment components, and obtain one-sided Likelihood Ratio analogues, whose asymptotic distribution we provide. We conduct Monte Carlo exercises to assess the finite sample properties of asymptotic and bootstrap versions of our tests. In an empirical application to CRSP stocks, we find that short-term reversals and momentum effects are better captured by non-Gaussian copulas. We estimate their parameters by indirect inference, and devise successful trading strategies.

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  • Dante Amengual & Enrique Sentana, 2015. "Is a Normal Copula the Right Copula?," Working Papers wp2015_1504, CEMFI.
    • Handle: RePEc:cmf:wpaper:wp2015_1504
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    1. Y. Malevergne & D. Sornette, 2003. "Testing the Gaussian copula hypothesis for financial assets dependences," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 231-250.
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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. Oh, Dong Hwan & Patton, Andrew J., 2023. "Dynamic factor copula models with estimated cluster assignments," Journal of Econometrics, Elsevier, vol. 237(2).
    3. 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.
    4. Fiorentini, Gabriele & Sentana, Enrique, 2021. "New testing approaches for mean–variance predictability," Journal of Econometrics, Elsevier, vol. 222(1), pages 516-538.
    5. 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.

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    More about this item

    Keywords

    Cokurtosis; coskewness; indirect inference; Kuhn-Tucker test; momentum strategies; non-linear dependence; short-term reversals; supremum test; underidentified parameters.;
    All these keywords.

    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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