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Local Gaussian correlation: A new measure of dependence

  • Tjøstheim, Dag
  • Hufthammer, Karl Ove
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    It is a common view among finance analysts and econometricians that the correlation between financial objects becomes stronger as the market is going down, and that it approaches one when the market crashes, having the effect of destroying the benefit of diversification. The purpose of this paper is to introduce a local dependence measure that gives a precise mathematical description and interpretation of such phenomena. We propose a new local dependence measure, a local correlation function, based on approximating a bivariate density locally by a family of bivariate Gaussian densities using local likelihood. At each point the correlation coefficient of the approximating Gaussian distribution is taken as the local correlation. Existence, uniqueness and limit results are established. A number of properties of the local Gaussian correlation and its estimate are given, along with examples from both simulated and real data. This new method of modelling carries with it the prospect of being able to do locally for a general density what can be done globally for the Gaussian density. In a sense it extends Gaussian analysis from a linear to a non-linear environment.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304407612001741
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    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 172 (2013)
    Issue (Month): 1 ()
    Pages: 33-48

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    Handle: RePEc:eee:econom:v:172:y:2013:i:1:p:33-48
    Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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    1. François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04.
    2. Frahm, Gabriel & Junker, Markus & Schmidt, Rafael, 2005. "Estimating the tail-dependence coefficient: Properties and pitfalls," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 80-100, August.
    3. Tjøstheim, Dag, 1986. "Estimation in nonlinear time series models," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 251-273, February.
    4. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(03), pages 726-748, June.
    5. Campbell, Rachel A.J. & Forbes, Catherine S. & Koedijk, Kees G. & Kofman, Paul, 2008. "Increasing correlations or just fat tails?," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 287-309, March.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Rodriguez, Juan Carlos, 2007. "Measuring financial contagion: A Copula approach," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 401-423, June.
    8. P. Silvapulle & C. W. J. Granger, 2001. "Large returns, conditional correlation and portfolio diversification: a value-at-risk approach," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 542-551.
    9. Jones, M. C., 1998. "Constant Local Dependence," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 148-155, February.
    10. Inci, A. Can & Li, H.C. & McCarthy, Joseph, 2011. "Financial contagion: A local correlation analysis," Research in International Business and Finance, Elsevier, vol. 25(1), pages 11-25, January.
    11. Kristin J. Forbes & Roberto Rigobon, 2002. "No Contagion, Only Interdependence: Measuring Stock Market Comovements," Journal of Finance, American Finance Association, vol. 57(5), pages 2223-2261, October.
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