Testing the Gaussian copula hypothesis for financial assets dependences

By Yannick Malevergne, Didier Sornette. 2001

253 citations recorded by the source corpus.

Abstract Using one of the key properties of copulas that they remain invariant under an arbitrary monotonic change of variable, we investigate the null hypothesis that the dependence between financial assets can be modelled by the Gaussian copula. We find that most pairs of currencies and pairs of major stocks are compatible with the Gaussian copula hypothesis, while this hypothesis can be rejected for the dependence between pairs of commodities (metals). Notwithstanding the apparent qualification of the Gaussian copula hypothesis for most of the currencies and the stocks, a non-Gaussian copula, such as the Student copula, cannot be rejected if it has sufficiently many ‘degrees of freedom’. As a consequence, it may be very dangerous to embrace blindly the Gaussian copula hypothesis, especially when the coefficient of correlation between the pairs of assets is too high, such that the tail dependence neglected by the Gaussian copula can became large, leading to the ignoring of extreme events which may occur in unison.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/55291394e34217ae404aef4c6b5a39b837663f89

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Citations in the corpus

Testing Goodness of Fit for Parametric Families of Copulas—Application to Financial Data (2005, background): “Various authors have addressed this question (see e.g., Breymann et al., 2003; Fermanian, 2003; Junker and May, 2002; Malevergne and Sornette, 2003; Mashal and Zeevi, 2002; Savu and Trede, 2004).”
Conditional dependence structure between oil prices and exchange rates: A copula-GARCH approach (2013, background): “Raw returns versus filtered returns Malevergne and Sornette (2003) suggest that the dependence structure of a copula is not the same for raw returns and filtered returns (residuals).”
Modeling the spatial dependence of floods using the Fisher copula (2019, methodology): “However, the Gaussian copula does not have tail dependence (Malevergne and Sornette, 2003) and the dependence is symmetrical (Bárdossy and Li, 2008 2.”
Copula-Based Models for Financial Time Series (2009, methodology): “Fermanian (2005) and Scaillet (2007) consider such an approach for models based on iid data, while Malevergne and Sornette (2003) and Panchenko (2005a) consider tests for time series models.”
The Joint Distribution of Stock Returns is Not Elliptical (2010, unknown): “Our methodology differs from usual hypothesis testing using statistical tools and goodness of fit tests, as can be encountered for example in [29] for testing the Gaussian copula hypothesis on financial assets.”
Goodness-of-fit tests for parametric families of Archimedean copulas (2008, background): “A slightly different approach is proposed by Malevergne and Sornette (2003), who test the Gaussian copula hypothesis for the bivariate case.”
The Euro and European Financial Market Dependence (2007, background): “Malevergne and Sornette (2003) demonstrate that returns from most pairs of major stock indices are compatible with the Gaussian copula.”
Simple Tests for Models of Dependence between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates (2004, methodology): “More generally, tail independence (i.e., τ L = 0, τU = 0) is not equivalent to independence in the tail (i.e., limy1,y2{H(y1, y2)/[F1(y1)F2(y2)]} = 1), see e.g. Malevergne and Sornette (2003). as the dimension of the copula under analysis is increased.”
Uncertainty and Crude Oil Returns (2016, background): “Malevergne and Sornette (2003) suggest that the dependence structure of a copula differs for raw returns and filtered returns (residuals).”
Dynamic hedging with futures: A copula‐based GARCH model (2008, unknown): “This finding is consistent with the results of Malevergne and Sornette (2003) and Bartram et al. (2007), who demonstrate that returns from most pairs of major stock indices are compatible with the Gaussian copula.”
Goodness-of-fit tests for copulas: A review and a power study (2006, methodology): “(1) Procedures developed for testing specific dependence structures such as the Normal copula (Malevergne and Sornette, 2003) or the equally popular Clayton family, also referred to as the gamma frailty model in survival analysis (Shih, 1998; Glidden, 1999; Cui and Sun, 2004).”