Parameter estimation for pair-copula constructions

Bernoulli

Volumn 19, Issue 2, 2013, Pages 462-491

  Haff, Ingrid Hobæk ^a  

^a NORWEGIAN COMPUTING CENTER   (Norway)

Author keywords

Copulae; Efficiency; Empirical distribution functions; Hierarchical construction; Stepwise estimation; Vines

Indexed keywords

EID: 84878135288     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/12-BEJ413     Document Type: Article

References (41)

1. Aas, K., Czado, C., Frigessi, A. and Bakken, H. (2009). Pair-copula constructions of multiple dependence. Insurance Math. Econom. 44 182-198. MR2517884
2. Bedford, T. and Cooke, R.M. (2001). Probability density decomposition for conditionally dependent random variables modeled by vines. Ann. Math. Artif. Intell. 32 245-268. MR1859866
3. Bedford, T. and Cooke, R.M. (2002). Vines - a new graphical model for dependent random variables. Ann. Statist. 30 1031-1068. MR1926167
4. Berg, D. and Aas, K. (2009). Models for construction of multivariate dependence. European Journal of Finance 15 639-659.
5. Chen, X. and Fan, Y. (2006). Estimation of copula-based semiparametric time series models. J. Econometrics 130 307-335. MR2211797
6. Chollete, L., Heinen, A. and Valdesogo, A. (2009). Modeling international financial returns with a multivariate regime switching copula. Journal of Financial Econometrics 7 437-480.
7. Claeskens, G. and Hjort, N.L. (2008). Model Selection and Model Averaging. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge: Cambridge Univ. Press. MR2431297
8. Clayton, D.G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65 141-151. MR0501698
9. Czado, C. and Min, A. (2010). Bayesian inference for multivariate copulas using pair-copula constructions. Journal of Financial Econometrics 8 511-546.
10. Czado, C., Min, A., Baumann, T. and Dakovic, R. (2009). Pair-copula constructions for modeling exchange rate dependence. Unpublished manuscript.
11. Czado, C., Schepsmeier, U. and Min, A. (2010). Maximum likelihood estimation of mixed c-vines with application to exchange rates. Unpublished manuscript.
12. Dissmann, J., Brechmann, E., Czado, C. and Kurowicka, K. (2011). Selecting and estimating regular vine copulae and application to financial returns. Unpublished manuscript.
13. Fischer, M., Köck, C., Schlüter, S. andWeigert, F. (2007).Multivariate copula models at work: Outperforming the "desert island copula"? Technical Report 79, Universität Erlangen-Nürnberg, Lehrstuhl für Statistik und Ökonometrie.
14. Genest, C. (1987). Frank's family of bivariate distributions. Biometrika 74 549-555. MR0909358
15. Genest, C., Gerber, H.U., Goovaerts, M.J. and Laeven, R.J.A. (2009). Editorial to the special issue on modeling and measurement of multivariate risk in insurance and finance. Insurance Math. Econom. 44 143-145. MR2517879
16. Genest, C., Ghoudi, K. and Rivest, L.P. (1995). A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 82 543-552. MR1366280
17. Genest, C. and Rivest, L.P. (1993). Statistical inference procedures for bivariate Archimedean copulas. J. Amer. Statist. Assoc. 88 1034-1043. MR1242947
18. Hall, P. and Yao, Q. (2005). Approximating conditional distribution functions using dimension reduction. Ann. Statist. 33 1404-1421. MR2195640
19. Heinen, A. and Valdesogo, A. (2009). Asymmetric capm dependence for large dimensions: the canonical vine autoregressive model. CORE Discussion Paper (2009/69).
20. Hobæk Haff, I. (2012). Supplement to "Parameter estimation for pair-copula constructions." DOI:10.3150/12-BEJ413SUPPA, DOI:10.3150/12-BEJ413SUPPB.
21. Hobæk Haff, I., Aas, K. and Frigessi, A. (2010). On the simplified pair-copula construction - simply useful or too simplistic? J. Multivariate Anal. 101 1296-1310. MR2595309
22. Joe, H. (1996). Distributions with Fixed Marginals and Related Topics, Chapter Families of M-Variate Distributions with Given Margins and m(m- 1)/2 Dependence Parameters. Hayward, CA: IMS.
23. Joe, H. (1997). Multivariate Models and Dependence Concepts. Monographs on Statistics and Applied Probability 73. London: Chapman & Hall. MR1462613
24. Joe, H. (2005). Asymptotic efficiency of the two-stage estimation method for copula-based models. J. Multivariate Anal. 94 401-419. MR2167922
25. Joe, H., Li, H. and Nikoloulopoulos, A.K. (2010). Tail dependence functions and vine copulas. J. Multivariate Anal. 101 252-270. MR2557632
26. Joe, H. and Xu, J. (1996). The estimation method of inference functions for margins for multivariate models. Technical Report 166, Univ. British Columbia, Dept. Statistics.
27. Kim, G., Silvapulle, M.J. and Silvapulle, P. (2007). Comparison of semiparametric and parametric methods for estimating copulas. Comput. Statist. Data Anal. 51 2836-2850. MR2345609
28. Klaassen, C.A.J. and Wellner, J.A. (1997). Efficient estimation in the bivariate normal copula model: Normal margins are least favourable. Bernoulli 3 55-77. MR1466545
29. Kolbjørnsen, O. and Stien, M. (2008). D-vine creation of non-Gaussian random field. In Procedings of the Eight International Geostatistics Congress 399-408. Santiago, Chile: GECAMIN Ltd.
30. Kurowicka, D. and Cooke, R. (2006). Uncertainty Analysis with High Dimensional Dependence Modelling. Wiley Series in Probability and Statistics. Chichester: Wiley. MR2216540
31. Lehmann, E.L. (2004). Elements of Large-Sample Theory. Springer Texts in Statistics. New York: Springer.
32. McNeil, A.J., Frey, R. and Embrechts, P. (2005). Quantitative Risk Management: Concepts, Techniques and Tools. Princeton Series in Finance. Princeton, NJ: Princeton Univ. Press. MR2175089
33. Min, A. and Czado, C. (2010). Scomdy models based on pair-copula constructions with application to exchange rates. Unpublished manuscript.
34. Oakes, D. (1982). A model for association in bivariate survival data. J. Roy. Statist. Soc. Ser. B 44 414-422. MR0693242
35. Schirmacher, D. and Schirmacher, E. (2008). Multivariate dependence modeling using pair-copulas. Presented at The 2008 ERM Symposium, Chicago.
36. Shih, J.H. and Louis, T.A. (1995). Inferences on the association parameter in copula models for bivariate survival data. Biometrics 51 1384-1399. MR1381050
37. Sklar, M. (1959). Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8 229-231. MR0125600
38. Stacy, E.W. (1962). A generalization of the gamma distribution. Ann. Math. Statist. 33 1187-1192. MR0143277
39. Stute, W. (1986). On almost sure convergence of conditional empirical distribution functions. Ann. Probab. 14 891-901. MR0841591
40. Tsukahara, H. (2005). Semiparametric estimation in copula models. Canad. J. Statist. 33 357-375. MR2193980
41. Tsukahara, H. (2011). Personal communication.