Statistical inference for multivariate residual copula of garch models

Statistica Sinica

Volumn 19, Issue 1, 2009, Pages 53-70

  Chan, Ngai Hang ^a   Chen, Jian ^b   Chen, Xiaohong ^c,d   Fan, Yanqin ^e   Peng, Liang ^f  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b Sage SB Inc   (United States)

^c YALE UNIVERSITY   (United States)

^d SHANGHAI UNIVERSITY OF FINANCE AND ECONOMICS   (China)

^e VANDERBILT UNIVERSITY   (United States)

^f GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Copula; GARCH; Goodness of fit test; Pseudo maximum likelihood estimation; Residual empirical distribution

Indexed keywords

EID: 61749097762     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. Amemiya, T. (1985). Advanced Econometrics. Harvard University Press, Boston.
2. Bauwens, J., Laurent, S. and Rombouts, J. V. K. (2006). Multivariate GARCH models: a survey. J. Appl. Econometrics 21, 79-110.
3. Berkes, I. and Horváth, L. (2003). Limit results for the empirical process of squared residuals in GARCH models. Stochastic Process. Appl. 105, 271-298.
4. Breymann, W., Dias, A. and Embrechts, P. (2003). Dependence structures for multivariate high-frequency data in finance. Quantitative Finance 3, 1-16.
5. Chen, S. and Huang, T. (2007). Nonparametric estimation of copula functions for dependence modeling. Canad. J. Statist. 35, 265-282.
6. Chen, X. and Fan, Y. (2005). Pseudo-likelihood ratio tests for model selection in semiparametric multivariate copula models. Canad. J. Statist. 33, 389-414.
7. Chen, X. and Fan, Y. (2006a). Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification. J. Econometrics 135, 125-154.
8. Chen, X. and Fan, Y. (2006b). Semiparametric estimation of copula-based time series models. J. Econometrics 130, 307-335.
9. Chen, X., Fan, Y. and Tsyrennikov, V. (2006). Efficient estimation of semiparametric multi-variate copula models. J. Amer. Statist. Assoc. 101, 1228-1240.
10. Claeskens, G. and Van Keilegom, I. (2003). Bootstrap confidence bands for regression curves and their derivatives. Ann. Statist. 31, 1852-1884.
11. Csörgö, M. and Révész, P. (1975). A strong approximation of the multivariate empirical process. Studia Scientiarum Mathematicarum Hungarica 10, 427-434.
12. Fan, J., Wang, M. and Yao, Q. (2008), Modeling multivariate volatilities via conditionally uncorrelated components. J. Roy. Statist. Soc. Ser. B 70, 679-702.
13. Fermanian, J. D. (2005). Goodness-of-fit tests for copulas. J. Multivariate Anal. 95, 119-152.
14. Fermanian, J. D., Radulovic, D. and Wegkamp, M. (2004). Weak convergence of empirical copula processes. Bernoulli 10, 847-860.
15. Fermanian, J. D. and Scaillet, O. (2003). Nonparametric estimation of copulas for time series. J. Risk 5, 25-54.
16. Genest, C., Ghoudi, K. and Rivest, L. (1995). A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 82, 543-552.
17. Genest, C., Quessy, J.-F. and Rmillard, B. (2006). Goodness-of-fit procedures for copula models based on the probability integral transformation. Scand. J. Statist. 33, 337-366.
18. Giacomini, E., Hardie, W., Ignatieva, E. and Spokoiny, V. (2008). Inhomogeneous dependency modelling with time varying copulae. J. Business and Economic Statist. 26, in press.
19. Hall, P. and Yao, Q. (2003). Inference in ARCH and GARCH models. Econometrica 71, 285-317.
20. Hull, J. and White, A. (1998). Value at risk when daily changes in market variables are not normally distributed. J. Derivatives 5, 9-19.
21. Horváth, L., Kokoszka, P. and Teyssiére, G. (2001). Empirical process of the squared residuals of an ARCH sequence. Ann. Statist. 29, 445-469.
22. Joe, H. (1997). Multivariate Models and Dependence Concepts. Chapman and Hall, New York.
23. Klugman, S. A. and Parsa, R. (1999). Fitting bivariate loss distributions with copulas. Insurance: Mathematics and Economics 24, 139-148.
24. Koul, H. L. and Ling, S. (2006). Fitting an error distribution in some heteroscedastic time series models. Ann. Statist. 34, 994-1012.
25. McNeil, A. J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management: Concepts, Techniques and Tools. Princeton University Press, New Jersey.
26. Nelsen, R. B. (2005). An Introduction to Copulas. 2nd edition. Springer, New York.
27. Scaillet, O. (2007). Kernel based goodness-of-fit tests for copulas with fixed smoothing parameters. J. Multivariate Anal. 98, 533-543.
28. Vervaat, W. (1972). Functional central limit theorems for processes with positive drift and their inverses. Z. Wahrsch. Verw. Gebiete 23, 249-253.