A review of copula models for economic time series

Journal of Multivariate Analysis

Volumn 110, Issue , 2012, Pages 4-18

  Patton, Andrew J ^a  

^a DUKE UNIVERSITY   (United States)

Author keywords

Correlation; Inference; Multivariate models; Semiparametric estimation; Time series

Indexed keywords

EID: 84862012537     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2012.02.021     Document Type: Article

References (147)

1. Aas K., Czado C., Frigessi A., Bakken H. Pair-copula constructions of multiple dependence. Insurance Math. Econom. 2009, 44:182-198.
2. Abegaz F., Naik-Nimbalkar U.V. Modeling statistical dependence of Markov chains via copula models. J. Statist. Plann. Inference 2008, 138:1131-1146.
3. Acar E.F., Genest C., Nešlehová J. Beyond simplified pair-copula constructions. J. Multivariate Anal. 2012, 110:74-90.
4. Alexander C. Market Risk Analysis, Volume III 2008, Wiley, London.
5. Andersen T.G., Bollerslev T., Christoffersen P., Diebold F.X. Volatility and correlation forecasting. Handbook of Economic Forecasting, Vol. 1 2006, Elsevier, Oxford.
6. Ang A., Chen J. Asymmetric correlations of equity portfolios. J. Finan. Econ. 2012, 63:443-494.
7. Ausin M.C., Lopes H.F. Time-varying joint distribution through copulas. Comput. Statist. Data Anal. 2010, 54:2383-2399.
8. Bae K.-H., Karolyi G.A., Stulz R.M. A new approach to measuring financial contagion. Rev. Finan. Stud. 2003, 16:717-764.
9. Bartram S.M., Taylor S.J., Wang Y.-H. The Euro and European financial market dependence. J. Bank. Financ. 2007, 51:1461-1481.
10. Beare B.K. Copulas and temporal dependence. Econometrica 2010, 78:395-410.
11. B.K. Beare, Archimedean copulas and temporal dependence, Econom. Theory (in press).
12. B.K. Beare, J. Seo, Time irreversible copula-based Markov models, Working Paper, University of California, San Diego, 2012.
13. Bennett M.N., Kennedy J.E. Quanto pricing with copulas. J. Derivatives 2004, 12:26-45.
14. Berg D. Copula goodness-of-fit testing: an overview and power comparison. European J. Finance 2009, 15:675-701.
15. Berg D., Quessy J.-F. Local power analyses of goodness-of-fit tests for copulas. Scandinavian J. Statist. 2009, 36:389-412.
16. Bollerslev T. Generalized autoregressive conditional heteroskedasticity. J. Econometrics 1986, 31:307-327.
17. Bollerslev T. A conditionally heteroskedastic time series model for speculative prices and rates of return. Rev. Econom. Statist. 1987, 69:542-547.
18. Bonhomme S., Robin J.-M. Assessing the equalizing force of mobility using short panels: France, 1990-2000. Rev. Econom. Stud. 2009, 76:63-92.
19. C. Bontemps, B. Feunou, N. Meddahi, Testing distributional assumptions: the multivariate case, Working Paper, École d'économie de Toulouse, Toulouse, France, 2011.
20. Bouyé É., Salmon M. Dynamic copula quantile regressions and tail area dynamic dependence in forex markets. European J. Finance 2009, 15:721-750.
21. Breymann W., Dias A., Embrechts P. Dependence structures for multivariate high-frequency data in finance. Quant. Finance 2003, 3:1-16.
22. Busetti F., Harvey A. When is a copula constant? a test for changing relationships. J. Finan. Econ. 2011, 9:106-131.
23. Chan N.-H., Chen J., Chen X., Fan Y., Peng L. Statistical inference for multivariate residual copula of GARCH models. Statist. Sinica 2009, 19:53-70.
24. Chen Y.-T. Moment tests for density forecast evaluation in the presence of parameter estimation uncertainty. J. Forecast. 2011, 30:409-450.
25. Chen X., Fan Y. Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification. J. Econometrics 2006, 135:125-154.
26. Chen X., Fan Y. Estimation of copula-based semiparametric time series models. J. Econometrics 2006, 130:307-335.
27. Chen X., Fan Y., Tsyrennikov V. Efficient estimation of semiparametric multivariate copula models. J. Amer. Statist. Assoc. 2006, 101:1228-1240.
28. Chen X., Koenker R., Xiao Z. Copula-based nonlinear quantile autoregression. Econom. J. 2009, 12:50-67.
29. Chen X., Wu W.B., Yi Y. Efficient estimation of copula-based semiparametric Markov models. Ann. Statist. 2009, 37:4214-4253.
30. Cherubini U., Gobbi F., Mulinacci S., Romagnoli S. Dynamic Copula Methods in Finance 2012, Wiley, England.
31. Cherubini U., Luciano E. Value at risk trade-off and capital allocation with copulas. Econom. Notes 2011, 30:235-256.
32. Cherubini U., Luciano E., Vecchiato W. Copula Methods in Finance 2004, Wiley, England.
33. Chollete L., Heinen A., Valdesogo A. Modeling international financial returns with a multivariate regime-switching copula. J. Finan. Econ. 2009, 7:437-480.
34. Choros B., Ibragimov R., Permiakova E. Copula estimation. Workshop on Copula Theory and its Applications 2010, Springer, Berlin.
35. P. Christoffersen, V. Errunza, K. Jacobs, H. Langlois, Is the potential for international diversification disappearing?, Working Paper, Rotman School of Management, University of Toronto, Canada, 2011.
36. P. Christoffersen, H. Langlois, The joint dynamics of equity market factors, Working Paper, Rotman School of Management, University of Toronto, Canada, 2011.
37. Corradi V., Swanson N.R. Predictive density evaluation. Handbook of Economic Forecasting, Vol. 1 2006, North Holland, Amsterdam.
38. D. Creal, S.J. Koopman, A. Lucas, Generalized autoregressive score models with applications, J. Appl. Econometrics (in press).
39. Darsow W.F., Nguyen B. Copulas and Markov processes. Illinois J. Math. 1992, 36:600-642.
40. Daul S., Giorgi E.D., Lindskog F., McNeil A.J. The grouped t-copula with an application to credit risk. J. Risk 2003, 16:73-76.
41. Dearden L., Fitzsimons E., Goodman A., Kaplan G. Higher education funding reforms in England: the distributional effects and the shifting balance of costs. Econom. J. 2008, 118:100-125.
42. Demarta S., McNeil A.J. The t copula and related copulas. Internat. Statist. Rev. 2005, 73:111-129.
43. Denuit M., Dhaene J., Goovaerts M., Kaas R. Actuarial Theory for Dependent Risks: Measures, Orders and Models 2005, Wiley, England.
44. Dias A., Embrechts P. Modeling exchange rate dependence dynamics at different time horizons. J. Internat. Money Finance 2010, 29:1687-1705.
45. Diebold F.X., Hahn J., Tay A.S. Multivariate density forecast evaluation and calibration in financial risk management: high frequency returns on foreign exchange. Rev. Econom. Statist. 1999, 81:661-673.
46. Dudley E., Nimalendran M. Margins and hedge fund contagion. J. Finan. Quant. Anal. 2011, 46:1227-1257.
47. Duffie D. Measuring Corporate Default Risk 2011, Oxford University Press, Oxford.
48. Embrechts P., Höing A. Extreme VaR scenarios in higher dimensions. Extremes 2006, 9:177-192.
49. Embrechts P., Höing A., Juri A. Using copulae to bound the value-at-risk for functions of dependent risks. Finance Stoch. 2003, 7:145-167.
50. Embrechts P., McNeil A.J., Straumann D. Correlation and dependence properties in risk management: properties and pitfalls. Risk Management: Value at Risk and Beyond 2002, Cambridge University Press, Cambridge.
51. Engle R.F. Autoregressive conditional heteroscedasticity with estimates of the variance of UK inflation. Econometrica 1982, 50:987-1007.
52. Engle R.F. Dynamic conditional correlation-a simple class of multivariate GARCH models. J. Bus. Econom. Statist. 2002, 20:339-350.
53. Erb C.B., Harvey C.R., Viskanta T.E. Forecasting international equity correlations. Financ. Anal. J. 1994, 50:32-45.
54. Ferguson T.S., Genest C., Hallin M. Kendall's tau for serial dependence. Canad. J. Statist. 2000, 28:587-604.
55. Fermanian J.-D., Radulović D., Wegkamp M.H. Weak convergence of empirical copula processes. Bernoulli 2004, 10:847-860.
56. Fermanian J.-D., Scaillet O. Nonparametric estimation of copulas for time series. J. Risk 2003, 5:25-54.
57. Fermanian J.-D., Wegkamp M.H. Time-dependent copulas. J. Multivariate Anal. 2012, 110:19-29.
58. Fisher R.A. Statistical Methods for Research Workers 1932, Oliver & Boyd, Edinburgh.
59. Frees E.W., Wang P. Copula credibility for aggregate loss models. Insurance Math. Econom. 2006, 38:360-373.
60. R. Frey, A.J. McNeil, Modelling dependent defaults, , 2001. http://e-collection.ethbib.ethz.ch/show?type%3Dbericht%26nr%3D273.
61. Gagliardini P., Gouriéroux C. Duration time-series models with proportional hazard. J. Time Ser. Anal. 2007, 29:74-124.
62. Gaißer S., Ruppert M., Schmid F. A multivariate version of Hoeffding's phi-square. J. Multivariate Anal. 2010, 101:2571-2586.
63. Garcia R., Tsafack G. Dependence structure and extreme comovements in international equity and bond markets. J. Bank. Financ. 2011, 35:1954-1970.
64. Genest C. Frank's family of bivariate distributions. Biometrika 1987, 74:549-555.
65. Genest C., Favre A.-C. Everything you always wanted to know about copula modeling but were afraid to ask. J. Hydraul. Eng. 2007, 12:347-368.
66. Genest C., Ghoudi K., Rivest L.-P. A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. Biometrika 1995, 82:543-552.
67. Genest C., Nešlehová J. A primer on copulas for count data. ASTIN Bull. 2007, 37:475-515.
68. Genest C., Nešlehová J., Ghorbal N.Ben Estimators based on Kendall's tau in multivariate copula models. Aust. N. Z. J. Stat. 2011, 53:157-177.
69. Genest C., Nešlehová J., Ziegel J. Inference in multivariate Archimedean copula models (with discussion). TEST 2011, 20:223-292.
70. Genest C., Rémillard B. Tests of independence and randomness based on the empirical copula process. TEST 2004, 13:335-369.
71. Genest C., Rémillard B. Validity of the parametric bootstrap for goodness-of-fit testing in semiparametric models. Ann. Inst. H. Poincaré Probab. Statist. 2008, 44:1096-1127.
72. Genest C., Rémillard B., Beaudoin D. Goodness-of-fit tests for copulas: a review and a power study. Insurance Math. Econom. 2009, 44:199-213.
73. Genest C., Rivest L.-P. Statistical inference procedures for bivariate Archimedean copulas. J. Amer. Statist. Assoc. 1993, 88:1034-1043.
74. Genest C., Segers J. Rank-based inference for bivariate extreme-value copulas. Ann. Statist. 2009, 37:2990-3022.
75. Ghoudi K., Rémillard B. Empirical processes based on pseudo-observations II: the multivariate case. Asymptotic Methods in Stochastics: Festschrift for Miklós Csörgo 2004, Amer. Math. Soc., Providence, RI.
76. Giacomini E., Härdle W., Spokoiny V. Inhomogeneous dependence modeling with time-varying copulae. J. Bus. Econom. Statist. 2009, 27:224-234.
77. Giesecke K. Correlated default with incomplete information. J. Bank. Financ. 2004, 28:1521-1545.
78. Glosten L.R., Jagannathan R., Runkle D.E. On the relation between the expected value and the volatility of the nominal excess return on stocks. J. Financ. 1993, 48:1779-1801.
79. Gonçalves S., White H. Maximum likelihood and the bootstrap for nonlinear dynamic models. J. Econometrics 2004, 119:199-220.
80. Gouriéroux C., Monfort A., Trognon A. Pseudo-maximum likelihood methods: theory. Econometrica 1984, 52:681-700.
81. Granger C.W.J., Teräsvirta T., Patton A.J. Common factors in conditional distributions for bivariate time series. J. Econometrics 2006, 132:43-57.
82. Grégoire V., Genest C., Gendron M. Using copulas to model price dependence in energy markets. Energy Risk 2008, 5:58-64.
83. Guégan D., Zhang J. Change analysis of dynamic copula for measuring dependence in multivariate financial data. Quant. Finance 2009, 10:421-430.
84. Hafner C.M., Manner H. Dynamic stochastic copula models: estimation, inference and applications. J. Appl. Econometrics 2012, 27:269-295.
85. Hamilton J.D. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 1989, 57:357-384.
86. Hansen B.E. Autoregressive conditional density estimation. Internat. Econom. Rev. 1994, 35:705-730.
87. Harvey A. Tracking a changing copula. J. Emp. Financ. 2010, 17:485-500.
88. Heinen A., Rengifo E. Multivariate autoregressive modeling of time series count data using copulas. J. Emp. Financ. 2007, 14:564-583.
89. A. Heinen, A. Valdesogo, Asymmetric CAPM dependence for large dimensions: the canonical vine autoregressive model, Discussion Paper 2009-069, Center for Operations Research and Econometrics, Université catholique de Louvain, Louvain-la-Neuve, Belgium, 2009.
90. Hering C., Hofert M., Mai J.-F., Scherer M. Constructing hierarchical Archimedean copulas with Lévy subordinators. J. Multivariate Anal. 2010, 101:1428-1433.
91. Hofert M., Mächler M., McNeil A.J. Likelihood inference for Archimedean copulas in high dimensions under known margins. J. Multivariate Anal. 2012, 110:133-150.
92. Hofert M., Scherer M. CDO pricing with nested Archimedean copulas. Quant. Finance 2011, 11:775-787.
93. Hong Y., Tu J., Zhou G. Asymmetries in stock returns: statistical tests and economic evaluation. Rev. Finan. Stud. 2007, 20:1547-1581.
94. Hull J., White A. Value at risk when daily changes in market variables are not normally distributed. J. Derivatives 1998, 5:9-19.
95. Ibragimov R. Copula-based characterizations for higher-order Markov processes. Econometric Theory 2009, 25:819-846.
96. R. Ibragimov, G. Lentzas, Copulas and long memory, harvard institute of economic research, Discussion Paper No. 2160, 2009.
97. Joe H. Asymptotic efficiency of the two-stage estimation method for copula-based models. J. Multivariate Anal. 1995, 94:401-419.
98. Joe H. Multivariate Models and Dependence Concepts 1997, Chapman & Hall, London.
99. H. Joe, J.J. Xu, The estimation method of inference functions for margins for multivariate models, Working Paper, Department of Statistics, University of British Columbia, Vancouver, Canada, 1996.
100. Jondeau É., Rockinger M. The copula-GARCH model of conditional dependencies: an international stock market application. J. Internat. Money Finance 2006, 25:827-853.
101. Kang B.U., In F., Kim G., Kim Y.S. A longer look at the asymmetric dependence between hedge funds and the equity market. J. Finan. Quant. Anal. 2010, 45:763-789.
102. Klaassen C.A.J., Wellner J.A. Efficient estimation in the bivariate normal copula model: normal margins are least favourable. Bernoulli 1997, 3:55-77.
103. Komunjer I. Quantile prediction. Handbook of Economic Forecasting, Vol. 2 2011, Elsevier, Oxford.
104. Lee T.-H., Long X. Copula-based multivariate GARCH model with uncorrelated dependent standardized returns. J. Econometrics 2009, 150:207-218.
105. Li D.X. On default correlation: a copula function approach. J. Fixed Income 2000, 9:43-54.
106. Longin F., Solnik B. Extreme correlation of international equity markets. J. Financ. 2001, 56:649-676.
107. H. Manner, O. Reznikova, A survey on time-varying copulas: specification, simulations and estimation, Econometric Rev. (2012) (in press).
108. Manner H., Segers J. Tails of correlation mixtures of elliptical copulas. Insurance Math. Econom. 2011, 48:153-160.
109. T.D. Markwat, E. Kole, D.J.C. van Dijk, Time variation in asset return dependence: strength or structure?, Working Paper, Econometric Institute, Erasmus University Rotterdam, The Netherlands, 2009.
110. McNeil A.J., Frey R., Embrechts P. Quantitative Risk Management: Concepts, Techniques and Tools 2005, Princeton University Press, Princeton, NJ.
111. Min A., Czado C. Bayesian inference for multivariate copulas using pair-copula constructions. J. Financ. Econ. 2010, 8:450-480.
112. Nelsen R.B. An Introduction to Copulas 2006, Springer. second ed.
113. Newey W.K., McFadden D. Large sample estimation and hypothesis testing. Handbook of Econometrics 1994, North-Holland, Amsterdam.
114. D.-H. Oh, A.J. Patton, Modelling dependence in high dimensions with factor copulas, Working Paper, Duke University, Durham, NC, 2011.
115. D.-H. Oh, A.J. Patton, Simulated method of moments estimation for copula-based multivariate models, Working Paper, Duke University, Durham, NC, 2011.
116. Okimoto T. New evidence of asymmetric dependence structure in international equity markets. J. Finan. Quant. Anal. 2008, 43:787-815.
117. A.J. Patton, Applications of copula theory in financial econometrics, Unpublished Ph.D. Dissertation, University of California, San Diego, CA, 2002.
118. Patton A.J. On the out-of-sample importance of skewness and asymmetric dependence for asset allocation. J. Financ. Econ. 2004, 2:130-168.
119. Patton A.J. Estimation of multivariate models for time series of possibly different lengths. J. Appl. Econometrics 2006, 21:147-173.
120. Patton A.J. Modelling asymmetric exchange rate dependence. Internat. Econom. Rev. 2006, 47:527-556.
121. Patton A.J. Are "market neutral" hedge funds really market neutral?. Rev. Finan. Stud. 2009, 22:2495-2530.
122. Patton A.J. Copula methods for forecasting multivariate time series. Handbook of Economic Forecasting, Vol. 2 2011, Elsevier, Oxford.
123. Pitt M., Chan D., Kohn R.J. Efficient Bayesian inference for Gaussian copula regression models. Biometrika 2006, 93:537-554.
124. Politis D.N., Romano J.P. The stationary bootstrap. J. Amer. Statist. Assoc. 1994, 89:1303-1313.
125. B. Rémillard, Goodness-of-fit tests for copulas of multivariate time series, Working Paper, HEC Montréal, Canada, 2010.
126. Rémillard B., Papageorgiou N., Soustra F. Copula-based semiparametric models for multivariate time series. J. Multivariate Anal. 2012, 110:30-42.
127. Rodriguez J.C. Measuring financial contagion: a copula approach. J. Empirical Finance 2007, 14:401-423.
128. Rosenberg J.V. Nonparametric pricing of multivariate contingent claims. J. Derivatives 2003, 10:9-26.
129. Rosenberg J.V., Schuermann T. A general approach to integrated risk management with skewed, fat-tailed risks. J. Financ. Econ. 2006, 79:569-614.
130. M. Ruppert, Consistent testing for a constant copula under strong mixing based on the tapered block multiplier technique, Working Paper, Wirtschafts- und Sozialwissenschaftliche Fakultät, Universität zu Köln, Germany, 2011.
131. Salmon M., Schleicher C. Pricing multivariate currency options with copulas. Copulas: From Theory to Application in Finance 2006, Risk Books, London.
132. Sancetta A., Satchell S. The Bernstein copula and its applications to modeling and approximations of multivariate distributions. Econom. Theory 2004, 20:535-562.
133. P. Schönbucher, D. Schubert, Copula dependent default risk in intensity models, Working Paper, Universität Bonn, Germany, 2001.
134. Shephard N. Stochastic Volatility: Selected Readings 2005, Oxford University Press, Oxford.
135. Shih J.H., Louis T.A. Inferences on the association parameter in copula models for bivariate survival data. Biometrics 1995, 51:1384-1399.
136. Sklar A. Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 1959, 8:229-231.
137. M.S. Smith, Bayesian approaches to copula modelling, in: Hierarchical Models and MCMC: A Tribute to Adrian Smith, Oxford University Press (in press).
138. Smith M.S., Gan Q., Kohn R.J. Modeling dependence using skew t copulas: Bayesian inference and applications. J. Appl. Econometrics 2012, 27:500-522.
139. Smith M.S., Min A., Almeida C., Czado C. Modeling longitudinal data using a pair-copula decomposition of serial dependence. J. Amer. Statist. Assoc. 2010, 105:1467-1479.
140. Song P., Fan Y., Kalbfleisch J.D. Maximization by parts in likelihood inference. J. Amer. Statist. Assoc. 2005, 100:1145-1158.
141. Sun J., Frees E.W., Rosenberg M. Heavy-tailed longitudinal data modeling using copulas. Insurance Math. Econom. 2008, 42:817-830.
142. Taylor S.J., Wang Y. Option prices and risk-neutral densities for currency cross-rates. J. Futures Markets 2010, 30:324-360.
143. Tsukahara H. Semiparametric estimation in copula models. Canad. J. Statist. 2005, 33:357-375.
144. van den Goorbergh R., Genest C., Werker B.J.M. Multivariate option pricing using dynamic copula models. Insurance Math. Econom. 2005, 37:101-114.
145. White H. Estimation, Inference and Specification Analysis 1994, Cambridge University Press, Cambridge.
146. Yi W., Liao S.S. Statistical properties of parametric estimators for Markov chain vectors on copula models. J. Statist. Plann. Inference 2010, 140:1465-1480.
147. D. Zimmer, The role of copulas in the housing crisis, Rev. Econom. Statist. (2012) (in press).