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Goodness-of-fit test for specification of semiparametric copula dependence models

Author

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  • Zhang, Shulin
  • Okhrin, Ostap
  • Zhou, Qian M.
  • Song, Peter X.-K.
Abstract
This paper concerns goodness-of-fit tests for semiparametric copula models. Our contribution is two-fold: we first propose a new test constructed via the comparison between “in-sample” and “out-of-sample” pseudo-likelihoods. Under the null hypothesis that the copula model is correctly specified, we show that the proposed test statistic converges in probability to a constant equal to the dimension of the parameter space. We establish the asymptotic normality and investigate the local power of the test. We also extend the proposed test to the specification test of a class of multivariate time series models, and propose a new bootstrap procedure to establish the finite-sample null distribution, which is shown to have better control of type I error than the commonly used bootstrap. Secondly, we introduce a Bonferroni-based hybrid mechanism to combine several test statistics, which yields a useful test. This hybrid method is particularly appealing when there exists no single dominant optimal test. We conduct comprehensive simulation experiments to compare the proposed new test and hybrid approach with two of the best “blanket” tests in the literature. For illustration, we apply the proposed tests to analyze two real datasets.

Suggested Citation

  • Zhang, Shulin & Okhrin, Ostap & Zhou, Qian M. & Song, Peter X.-K., 2016. "Goodness-of-fit test for specification of semiparametric copula dependence models," Journal of Econometrics, Elsevier, vol. 193(1), pages 215-233.
    • Handle: RePEc:eee:econom:v:193:y:2016:i:1:p:215-233
    DOI: 10.1016/j.jeconom.2016.02.017
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    2. Jie Huang & Haiming Zhou & Nader Ebrahimi, 2022. "Bayesian Bivariate Cure Rate Models Using Copula Functions," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(3), pages 1-9, May.
    3. Klochkov, Yegor & Härdle, Wolfgang Karl & Xu, Xiu, 2019. "Localizing Multivariate CAViaR," IRTG 1792 Discussion Papers 2019-007, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    4. Bingduo Yang & Zongwu Cai & Christian M. Hafner & Guannan Liu, 2018. "Trending Mixture Copula Models with Copula Selection," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201809, University of Kansas, Department of Economics, revised Sep 2018.
    5. Qian M. Zhou, 2024. "Information matrix equivalence in the presence of censoring: a goodness-of-fit test for semiparametric copula models with multivariate survival data," Statistical Papers, Springer, vol. 65(7), pages 4677-4713, September.
    6. F. Marta L. Di Lascio & Andrea Menapace & Maurizio Righetti, 2020. "Joint and conditional dependence modelling of peak district heating demand and outdoor temperature: a copula-based approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 373-395, June.
    7. Tao Sun & Yi Liu & Richard J. Cook & Wei Chen & Ying Ding, 2019. "Copula-based score test for bivariate time-to-event data, with application to a genetic study of AMD progression," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 546-568, July.
    8. Shulin Zhang & Qian M. Zhou & Huazhen Lin, 2021. "Goodness-of-fit test of copula functions for semi-parametric univariate time series models," Statistical Papers, Springer, vol. 62(4), pages 1697-1721, August.
    9. Miriam Jaser & Aleksey Min, 2021. "On tests for symmetry and radial symmetry of bivariate copulas towards testing for ellipticity," Computational Statistics, Springer, vol. 36(3), pages 1-26, September.
    10. Gong Chen & Hartmut Fricke & Ostap Okhrin & Judith Rosenow, 2022. "Importance of Weather Conditions in a Flight Corridor," Stats, MDPI, vol. 5(1), pages 1-27, March.
    11. Poeschel, Friedrich, 2012. "Assortative matching through signals," VfS Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62061, Verein für Socialpolitik / German Economic Association.
    12. Fontaine, Charles & Frostig, Ron D. & Ombao, Hernando, 2020. "Modeling non-linear spectral domain dependence using copulas with applications to rat local field potentials," Econometrics and Statistics, Elsevier, vol. 15(C), pages 85-103.

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    More about this item

    Keywords

    Bootstrap hybrid test; In-and-out-of sample likelihood; Power;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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