Hostname: page-component-7479d7b7d-qlrfm Total loading time: 0 Render date: 2024-07-12T18:15:48.159Z Has data issue: false hasContentIssue false
  • English
  • Français

RANDOMIZATION TESTS OF COPULA SYMMETRY

Published online by Cambridge University Press:  06 April 2020

Brendan K. Beare  and
Juwon Seo
Brendan K. Beare
Affiliation:
University of Sydney
Juwon Seo*
Affiliation:
National University of Singapore
*
Address correspondence to Juwon Seo, Department of Economics, National University of Singapore, Singapore; e-mail: ecssj@nus.edu.sg
Get access Rights & Permissions [Opens in a new window]

Abstract

New nonparametric tests of copula exchangeability and radial symmetry are proposed. The novel aspect of the tests is a resampling procedure that exploits group invariance conditions associated with the relevant symmetry hypothesis. They may be viewed as feasible versions of randomization tests of symmetry, the latter being inapplicable due to the unobservability of marginals. Our tests are simple to compute, control size asymptotically, consistently detect arbitrary forms of asymmetry, and do not require the specification of a tuning parameter. Simulations indicate excellent small sample properties compared with existing procedures involving the multiplier bootstrap.

Type
ARTICLES
Information
Econometric Theory , Volume 36 , Issue 6 , December 2020 , pp. 1025 - 1063
Copyright
© Cambridge University Press 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

We thank Xiaohong Chen, Viktor Todorov, and seminar participants at the University of Seville, Korea University, and Yonsei University for helpful comments.

References

Ang, A. & Chen, J. (2002) Asymmetric correlations of equity portfolios. Journal of Financial Economics 63, 443–494.CrossRefGoogle Scholar
Athey, S. & Haile, P.A. (2002) Identification of standard auction models. Econometrica 70, 2107–2140.CrossRefGoogle Scholar
Bahraoui, T. & Quessy, J.-F. (2017) Tests of radial symmetry for multivariate copulas based on the copula characteristic function. Electronic Journal of Statistics 11, 2066–2096.CrossRefGoogle Scholar
Beare, B.K. & Seo, J. (2014) Time irreversible copula-based Markov models. Econometric Theory 30, 923–960.CrossRefGoogle Scholar
Bogachev, V.I. (1998) Gaussian Measures. American Mathematical Society, Providence, RI.CrossRefGoogle Scholar
Bouzebda, S. & Cherfi, M. (2012) Test of symmetry based on copula function. Journal of Statistical Planning and Inference 142, 1262–1271.CrossRefGoogle Scholar
Bücher, A. (2011) Statistical Inference for Copulas and Extremes. Doctoral thesis. Ruhr-Universität Bochum.Google Scholar
Bücher, A. & Dette, H. (2010) A note on bootstrap approximations for the empirical copula process. Statistics and Probability Letters 80, 1925–1932.CrossRefGoogle Scholar
Bücher, A., Irresberger, F., & Weiss, G.N.F. (2017) Testing asymmetry in dependence with copula-coskewness. North American Actuarial Journal 21, 267–280.CrossRefGoogle Scholar
Bücher, A. & Volgushev, S. (2013) Empirical and sequential copula processes under serial dependence. Journal of Multivariate Analysis 119, 61–70.CrossRefGoogle Scholar
Canay, I.A., Romano, J.P., & Shaikh, A. (2017) Randomization tests under an approximate symmetry assumption. Econometrica 85, 1013–1030.CrossRefGoogle Scholar
Carabarin-Aguirre, A. & Ivanoff, B.G. (2010) Estimation of a distribution under generalized censoring. Journal of Multivariate Analysis 101, 1501–1519.CrossRefGoogle Scholar
Chan, N.-H., Chen, J., Chen, X., Fan, Y., & Peng, L. (2009) Statistical inference for multivariate residual copula of GARCH models. Statistica Sinica 19, 53–70.Google Scholar
Chen, X. & Fan, Y. (2006) Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification. Journal of Econometrics 135, 125–154.CrossRefGoogle Scholar
Chen, Y. & Riordan, M.H. (2013) Profitability of product bundling. International Economic Review 54, 35–57.CrossRefGoogle Scholar
Chung, E. & Romano, J.P. (2013) Exact and asymptotically robust permutation tests. Annals of Statistics 41, 484–507.CrossRefGoogle Scholar
Chung, E. & Romano, J.P. (2016a) Asymptotically valid and exact permutation tests based on two-sample U-statistics. Journal of Statistical Planning and Inference 168, 97–105.CrossRefGoogle Scholar
Chung, E. & Romano, J.P. (2016b) Multivariate and multiple permutation tests. Journal of Econometrics 193, 76–91.CrossRefGoogle Scholar
Deheuvels, P. (1979) La fonction de dépendance empirique et ses propriétés: Un test non paramétrique d’indépendance. Académie Royale de Belgique, Bulletin de la Classe des Sciences 65, 274–292.Google Scholar
Dehgani, A., Dolati, A. & Úbeda-Flores, M. (2013) Measures of radial asymmetry for bivariate random vectors. Statistical Papers 54, 271–286.CrossRefGoogle Scholar
Fermanian, J.-D., Radulović, D., & Wegkamp, M. (2004) Weak convergence of empirical copula processes. Bernoulli 10, 847–860.CrossRefGoogle Scholar
Garcia, R. & Tsafack, G. (2011) Dependence structure and extreme comovements in international equity and bond markets. Journal of Banking and Finance 35, 1954–1970.CrossRefGoogle Scholar
Genest, C. & Nešlehová, J.G. (2014) On tests of radial symmetry for bivariate copulas. Statistical Papers 55, 1107–1119.CrossRefGoogle Scholar
Genest, C., Nešlehová, J.G., & Quessy, J.-F. (2012) Tests of symmetry for bivariate copulas. Annals of the Institute of Statistical Mathematics 64, 811–834.CrossRefGoogle Scholar
Harder, M. & Stadtmüller, U. (2017) Testing exchangeability of copulas in arbitrary dimension. Journal of Nonparametric Statistics 29, 40–60.CrossRefGoogle Scholar
Hendricks, K., Pinske, J., & Porter, R.H. (2003) Empirical implications of equilibrium bidding in first-price, symmetric common value auctions. Review of Economic Studies 70, 115–145.CrossRefGoogle Scholar
Hoeffding, W. (1952) The large-sample power of tests based on permutations of observations. Annals of Mathematical Statistics 23, 169–192.CrossRefGoogle Scholar
Hong, Y., Tu, J., & Zhou, G. (2007) Asymmetries in stock returns: Statistical tests and economic evaluation. Review of Financial Studies 20, 1547–1581.CrossRefGoogle Scholar
Khoudraji, A. (1995) Contributions à l’étude des copules et à la modélisation de valeurs extrêmes bivariées. Ph.D. thesis, Université Laval, Québec City, Canada.Google Scholar
Kosorok, M.R. (2008) Introduction to Empirical Processes and Semiparametric Inference. Springer Series in Statistics, New York, NY.CrossRefGoogle Scholar
Krupskii, P. (2017) Copula-based measures of reflection and permutation asymmetry and statistical tests. Statistical Papers 58, 1165–1187.CrossRefGoogle Scholar
Li, B. & Genton, M.G. (2013) Nonparametric identification of copula structures. Journal of the American Statistical Association 108, 666–675.CrossRefGoogle Scholar
Li, T., Perrigne, I., & Vuong, Q. (2000) Conditionally independent private information in OCS wildcat auctions. Journal of Econometrics 98, 129–161.CrossRefGoogle Scholar
Menzel, K. (2016) Inference for games with many players. Review of Economic Studies 83, 306–337.CrossRefGoogle Scholar
Milgrom, P.R. & Weber, R.J. (1982) A theory of auctions and competitive bidding. Econometrica 50, 1089–1122.CrossRefGoogle Scholar
Nelsen, R.B. (1993) Some concepts of bivariate symmetry. Journal of Nonparametric Statistics 3, 95–101.CrossRefGoogle Scholar
Nelsen, R.B. (2006) An Introduction to Copulas, 2nd edn. Springer, New York, NY.Google Scholar
Nelsen, R.B. (2007) Extremes of nonexchangeability. Statistical Papers 48, 329–336.CrossRefGoogle Scholar
Okimoto, T. (2008) New evidence of asymmetric dependence structures in international equity markets. Journal of Financial and Quantitative Analysis 43, 787–815.CrossRefGoogle Scholar
Patton, A.J. (2004) On the out-of-sample importance of skewness and asymmetric dependence for asset allocation. Journal of Financial Econometrics 2, 130–168.CrossRefGoogle Scholar
Patton, A.J. (2006) Modelling asymmetric exchange rate dependence. International Economic Review 47, 527–556.CrossRefGoogle Scholar
Pollard, D. (1990) Empirical Processes: Theory and Applications. Institute of Mathematical Statistics, Hayward, CA.Google Scholar
Quessy, J.-F. (2016) On consistent nonparametric statistical tests of symmetry hypotheses. Symmetry 8, 31.CrossRefGoogle Scholar
Quessy, J.-F. & Bahraoui, T. (2013) Graphical and formal statistical tools for the symmetry of bivariate copulas. Canadian Journal of Statistics 41, 637–656.CrossRefGoogle Scholar
Rémillard, B. & Scaillet, O. (2009) Testing for equality between two copulas. Journal of Multivariate Analysis 100, 377–386.CrossRefGoogle Scholar
Romano, J.P. (1989) Bootstrap and randomization tests of some nonparametric hypotheses. Annals of Statistics 17, 141–159.CrossRefGoogle Scholar
Romano, J.P. (1990) On the behavior of randomization tests without a group invariance assumption. Journal of the American Statistical Association 85, 686–692.CrossRefGoogle Scholar
Rüschendorf, L. (1976) Asymptotic distributions of multivariate rank order statistics. Annals of Statistics 4, 912–923.CrossRefGoogle Scholar
Segers, J. (2012) Asymptotics of empirical copula processes under non-restrictive smoothness assumptions. Bernoulli 18, 764–782.Google Scholar
Seo, J. (2020) Randomization tests for equality in dependence structure. Journal of Business and Economic Statistics (in press).CrossRefGoogle Scholar
Sklar, A. (1959) Fonctions de répartition à n dimensions et leurs marges. Publications of the Institute of Statistics of the University of Paris 8, 229–231.Google Scholar
Tang, X. (2011) Bounds on revenue distributions in counterfactual auctions with reserve prices. RAND Journal of Economics 42, 175–203.CrossRefGoogle Scholar