Simple Tests for Models of Dependence between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates

London Economics Financial Markets Group Working Paper No. 483

37 Pages Posted: 6 Mar 2004

See all articles by Xiaohong Chen

Xiaohong Chen

Yale University - Cowles Foundation

Yanqin Fan

Vanderbilt University - College of Arts and Science - Department of Economics

Andrew J. Patton

Duke University - Department of Economics

Date Written: January 2004

Abstract

Evidence that asset returns are more highly correlated during volatile markets and during market downturns (see Longin and Solnik, 2001, and Ang and Chen, 2002) has lead some researchers to propose alternative models of dependence. In this paper we develop two simple goodness-of-fit tests for such models. We use these tests to determine whether the multivariate Normal or the Student's t copula models are compatible with U.S. equity return and exchange rate data. Both tests are robust to specifications of marginal distributions, and are based on the multivariate probability integral transform and kernel density estimation. The first test is consistent but requires the estimation of a multivariate density function and is recommended for testing the dependence structure between a small number of assets. The second test may not be consistent against all alternatives but it requires kernel estimation of only a univariate density function, and hence is useful for testing the dependence structure between a large number of assets. We justify our tests for both observable multivariate strictly stationary time series and for standardized innovations of GARCH models. A simulation study demonstrates the efficacy of both tests. When applied to equity return data and exchange rate return data, we find strong evidence against the normal copula, but little evidence against the more flexible Student's t copula.

Keywords: Copulas, correlation, nonlinear comovements, goodness-of-fit tests, GARCH

JEL Classification: C52, C32, C14

Suggested Citation

Chen, Xiaohong and Fan, Yanqin and Patton, Andrew J., Simple Tests for Models of Dependence between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates (January 2004). London Economics Financial Markets Group Working Paper No. 483, Available at SSRN: https://ssrn.com/abstract=513024 or http://dx.doi.org/10.2139/ssrn.513024

Xiaohong Chen (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Yanqin Fan

Vanderbilt University - College of Arts and Science - Department of Economics ( email )

Box 1819 Station B
Nashville, TN 37235
United States

Andrew J. Patton

Duke University - Department of Economics ( email )

213 Social Sciences Building
Box 90097
Durham, NC 27708-0204
United States

HOME PAGE: http://econ.duke.edu/~ap172/

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