zbMATH — the first resource for mathematics

Testing goodness of fit for parametric families of copulas — application to financial data. (English) Zbl 1080.62040
Summary: This article suggests a chi-square test of fit for parametric families of bivariate copulas. The marginal distribution functions are assumed to be unknown and are estimated by their empirical counterparts. Therefore, the standard asymptotic theory of the test is not applicable, but we derive a rule for the determination of the appropriate degrees of freedom in the asymptotic chi-square distribution. The behavior of the test under $$H_{0}$$ and for selected alternatives is investigated by Monte Carlo simulations. The test is applied to investigate the dependence structure of daily German asset returns. It turns out that the Gauss copula is inappropriate to describe the dependencies in the data. A $$t_{\nu}$$-copula with low degrees of freedom performs better.

MSC:
 62H15 Hypothesis testing in multivariate analysis 62H10 Multivariate distribution of statistics 65C05 Monte Carlo methods 62P05 Applications of statistics to actuarial sciences and financial mathematics 62H05 Characterization and structure theory for multivariate probability distributions; copulas
Full Text:
References:
 [1] DOI: 10.1080/713666155 [2] DOI: 10.1016/j.jmva.2004.07.004 · Zbl 1095.62052 [3] Greenwood P. E., A Guide to Chi-Squared Testing (1996) [4] Joe H., Multivariate Models and Dependence Concepts (1997) · Zbl 0990.62517 [5] Junker M., The Econometrics Journal (2002) [6] DOI: 10.1088/1469-7688/3/4/301 [7] Mashal R., Beyond Correlation: Extreme Co-movements Between Financial Assets (2002) [8] DOI: 10.1007/3-540-48236-9 [9] Savu , C. , Trede , M. ( 2004 ). Goodness-of-fit tests for parametric families of Archimedian copulas . Beiträge zur angewandten Wirtschaftforschung, CAWM , Münster University . http://www.cawm.de · Zbl 1134.91556
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.