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Semiparametric Conditional Mixture Copula Models with Copula Selection

Author

Listed:
  • Zongwu Cai

    (Department of Economics, The University of Kansas, Lawrence, KS 66045, USA)

  • Guannan Liu

    (School of Economics and WISE, Xiamen University, Xiamen, Fujian 361005, China)

  • Wei Long

    (Department of Economics, Tulane University, New Orleans, LA 70118, USA)

  • Xuelong Luo

    (School of Economics and WISE, Xiamen University, Xiamen, Fujian 361005, China)

Abstract

This study proposes a semiparametric conditional mixture copula model, that allows for unspecified functions of a covariate in both the (conditional) marginal distributions and the copula dependence and weight parameters. To estimate this model, we propose a two-step procedure. In the first step, the (conditional) marginal distributions are nonparametrically estimated using the weighted Nadaraya- Watson method. In the second step, we apply a penalized local log-likelihood function with a penalty term to simultaneously estimate the copula parameters and choose an appropriate copula model. Furthermore, we propose a test of covariate effects for time series data. We establish the large sample properties of both the penalized and unpenalized estimators based on alpha-mixing conditions. Monte Carlo simulations show that the proposed method performs well in selecting and estimating conditional mixture copulas under various model specifications. Finally, we apply the proposed method to investigate the dynamic patterns of dependence among four states' housing markets along the interest rate path.

Suggested Citation

  • Zongwu Cai & Guannan Liu & Wei Long & Xuelong Luo, 2024. "Semiparametric Conditional Mixture Copula Models with Copula Selection," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202401, University of Kansas, Department of Economics, revised Jan 2024.
  • Handle: RePEc:kan:wpaper:202401
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    References listed on IDEAS

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    1. Zongwu Cai & Xian Wang, 2014. "Selection of Mixed Copula Model via Penalized Likelihood," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 788-801, June.
    2. Liu, Guannan & Long, Wei & Zhang, Xinyu & Li, Qi, 2019. "Detecting Financial Data Dependence Structure By Averaging Mixture Copulas," Econometric Theory, Cambridge University Press, vol. 35(4), pages 777-815, August.
    3. Guannan Liu & Wei Long & Bingduo Yang & Zongwu Cai, 2022. "Semiparametric estimation and model selection for conditional mixture copula models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 287-330, March.
    4. Almeida, Carlos & Czado, Claudia, 2012. "Efficient Bayesian inference for stochastic time-varying copula models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1511-1527.
    5. Bingduo Yang & Christian M. Hafner & Guannan Liu & Wei Long, 2021. "Semiparametric estimation and variable selection for single‐index copula models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(7), pages 962-988, November.
    6. Elif F. Acar & Radu V. Craiu & Fang Yao, 2011. "Dependence Calibration in Conditional Copulas: A Nonparametric Approach," Biometrics, The International Biometric Society, vol. 67(2), pages 445-453, June.
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    8. Christian M. Hafner & Hans Manner, 2012. "Dynamic stochastic copula models: estimation, inference and applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(2), pages 269-295, March.
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    13. Fermanian, Jean-David & Wegkamp, Marten H., 2012. "Time-dependent copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 19-29.
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    More about this item

    Keywords

    Conditional Copula; Mixture Copula; Semiparametric Estimation; Copula Selection; SCAD; EM algorithm.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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