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Local Gaussian correlation: A new measure of dependence

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  • Tjøstheim, Dag
  • Hufthammer, Karl Ove

Abstract

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.

Suggested Citation

  • Tjøstheim, Dag & Hufthammer, Karl Ove, 2013. "Local Gaussian correlation: A new measure of dependence," Journal of Econometrics, Elsevier, vol. 172(1), pages 33-48.
  • Handle: RePEc:eee:econom:v:172:y:2013:i:1:p:33-48
    DOI: 10.1016/j.jeconom.2012.08.001
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Georgios Bampinas & Theodore Panagiotidis, 2017. "Oil and stock markets before and after financial crises: A local Gaussian correlation approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(12), pages 1179-1204, December.
    2. Otneim, Håkon & Tjøstheim, Dag, 2016. "Non-parametric estimation of conditional densities: A new method," Discussion Papers 2016/22, Norwegian School of Economics, Department of Business and Management Science.
    3. Akimitsu Inoue, 2016. "Density estimation based on pointwise mutual information," Economics Bulletin, AccessEcon, vol. 36(2), pages 1138-1148.
    4. Otneim, Håkon & Karlsen, Hans Arnfinn & Tjøstheim, Dag, 2013. "Bias and bandwidth for local likelihood density estimation," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1382-1387.
    5. Støve, Bård & Tjøstheim, Dag & Hufthammer, Karl Ove, 2014. "Using local Gaussian correlation in a nonlinear re-examination of financial contagion," Journal of Empirical Finance, Elsevier, vol. 25(C), pages 62-82.

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