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Efficient estimation of copula-GARCH models

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  • Liu, Yan
  • Luger, Richard

Abstract

An iterative (fixed-point) algorithm for the maximum-likelihood estimation of copula-based models that circumvents the need to compute second-order derivatives of the full likelihood function is adapted and examined. The algorithm exploits the structure of copula-based models that yield a natural decomposition of a potentially complicated likelihood function into two parts. The first part is a working likelihood that only involves the parameters of the marginals and the residual part is used to update estimates from the first part. A modified algorithm based on a working likelihood that accounts for some degree of correlation between the marginals is proposed. Compared to the original algorithm based on the working likelihood with the independent correlation, the modified one provides a better approximation to the full likelihood and overcomes convergence difficulties. A numerical example illustrates the efficiency gains of the estimation algorithms in the context of a benchmark copula-GARCH model. The modified algorithm is illustrated by an application to daily returns on two major stock market indices.

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  • Liu, Yan & Luger, Richard, 2009. "Efficient estimation of copula-GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2284-2297, April.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:6:p:2284-2297
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    2. Wang Ruihua & Wang Hongjun, 2020. "Correlation Analysis of Stock Market and Fund Market Based on M-Copula-EGARCH-M-GED Model," Journal of Systems Science and Information, De Gruyter, vol. 8(3), pages 240-252, June.
    3. Weiß, Gregor N.F. & Scheffer, Marcus, 2015. "Mixture pair-copula-constructions," Journal of Banking & Finance, Elsevier, vol. 54(C), pages 175-191.
    4. Taras Bodnar & Nikolaus Hautsch, 2012. "Copula-Based Dynamic Conditional Correlation Multiplicative Error Processes," SFB 649 Discussion Papers SFB649DP2012-044, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    6. Nikoloulopoulos, Aristidis K. & Joe, Harry & Li, Haijun, 2012. "Vine copulas with asymmetric tail dependence and applications to financial return data," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3659-3673.
    7. Arthur Charpentier, 2015. "Prévision avec des copules en finance," Working Papers hal-01151233, HAL.
    8. Alp, Tansel & Demetrescu, Matei, 2010. "Joint forecasts of Dow Jones stocks under general multivariate loss function," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2360-2371, November.
    9. Bodnar, Taras & Hautsch, Nikolaus, 2016. "Dynamic conditional correlation multiplicative error processes," Journal of Empirical Finance, Elsevier, vol. 36(C), pages 41-67.
    10. Bai, Xiwen & Lam, Jasmine Siu Lee, 2019. "A copula-GARCH approach for analyzing dynamic conditional dependency structure between liquefied petroleum gas freight rate, product price arbitrage and crude oil price," Energy Economics, Elsevier, vol. 78(C), pages 412-427.
    11. Gregor Weiß, 2013. "Copula-GARCH versus dynamic conditional correlation: an empirical study on VaR and ES forecasting accuracy," Review of Quantitative Finance and Accounting, Springer, vol. 41(2), pages 179-202, August.
    12. Brechmann, Eike C. & Hendrich, Katharina & Czado, Claudia, 2013. "Conditional copula simulation for systemic risk stress testing," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 722-732.
    13. Silva Filho, Osvaldo Candido da & Ziegelmann, Flavio Augusto & Dueker, Michael J., 2012. "Modeling dependence dynamics through copulas with regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 346-356.
    14. Yan Cui & Qi Li & Fukang Zhu, 2020. "Flexible bivariate Poisson integer-valued GARCH model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1449-1477, December.
    15. Brechmann Eike Christain & Czado Claudia, 2013. "Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50," Statistics & Risk Modeling, De Gruyter, vol. 30(4), pages 307-342, December.
    16. Zhang, Ran & Czado, Claudia & Min, Aleksey, 2011. "Efficient maximum likelihood estimation of copula based meta t-distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1196-1214, March.
    17. David T. Frazierz & Eric Renault, 2016. "Efficient Two-Step Estimation via Targeting," CIRANO Working Papers 2016s-16, CIRANO.
    18. 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.
    19. Paolella, Marc S. & Polak, Paweł, 2015. "ALRIGHT: Asymmetric LaRge-scale (I)GARCH with Hetero-Tails," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 282-297.
    20. Brechmann, Eike C. & Joe, Harry, 2015. "Truncation of vine copulas using fit indices," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 19-33.
    21. Martin Burda & Louis Belisle, 2019. "Copula Multivariate GARCH Model with Constrained Hamiltonian Monte Carlo," Working Papers tecipa-638, University of Toronto, Department of Economics.
    22. Burda Martin & Bélisle Louis, 2019. "Copula multivariate GARCH model with constrained Hamiltonian Monte Carlo," Dependence Modeling, De Gruyter, vol. 7(1), pages 133-149, January.
    23. Frazier, David T. & Renault, Eric, 2017. "Efficient two-step estimation via targeting," Journal of Econometrics, Elsevier, vol. 201(2), pages 212-227.
    24. Spanhel, Fabian & Kurz, Malte S., 2016. "The partial copula: Properties and associated dependence measures," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 76-83.
    25. Ausin, M. Concepcion & Lopes, Hedibert F., 2010. "Time-varying joint distribution through copulas," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2383-2399, November.

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