Test for Homogeneity of the Scale Matrix of Elliptical Tail Dependence with Application to Real Data
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In finance, random quantities such as returns frequently exhibit asymmetry in their tail behavior. The tail behavior is described using an elliptical distribution owing to its heaviness. Moreover, elliptical distributions constitute a parametric model class of multivariate regular variations, and the scale matrix is important in determining the tail dependence. For testing the asymmetry of the tail dependence, we propose a likelihood ratio test that checks the homogeneity of the scale matrix in separate regions. Moreover, the proposed test is applied to a real dataset to investigate the asymmetry of tail dependence.
Abstract
In finance, random quantities such as returns frequently exhibit asymmetry in their tail behavior. The tail behavior is described using an elliptical distribution owing to its heaviness. Moreover, elliptical distributions constitute a parametric model class of multivariate regular variations, and the scale matrix is important in determining the tail dependence. For testing the asymmetry of the tail dependence, we propose a likelihood ratio test that checks the homogeneity of the scale matrix in separate regions. Moreover, the proposed test is applied to a real dataset to investigate the asymmetry of tail dependence.
참고문헌 (9)
- Hult H, "Multivariate extremes, aggregation and dependence in elliptical distributions", Adv Appl Probab, 34, pp.587~608 (2002)
- Cai J-J, "Estimation of extreme risk regions under multivariate regular variation", Ann Stat, 39, pp.1803~1826 (2011)
- Einmahl JH, "Testing the multivariate regular variation model", J Bus Econ Stat, pp.1~13 (2020)
- 김종민, "A Review of Copula Methods for Measuring Uncertainty in Finance and Economics", Quantitative Bio-Science, 39(2), pp.81~90 (2020), 자연과학연구소[DOI]
- Lupelberg C, "Estimating the tail dependence function of an elliptical distribution", Bernoulli, 13, pp.299~251 (2007)
- Lupelberg C, "Semi-parametric models for the multivariate tail dependence function-the asymptotically depen-dent case", Scand J Stat, 35, pp.701~718 (2008)
- Kim M, "Maximum likelihood estimation of spectral measure of heavy tailed elliptical distribution", Proceeding of The Autumn Conference of the Korean Data & Information Science Society, pp.119~119 (2021)
- Wilks SS, "The large-sample distribution of the likelihood ratio for testing composite hypotheses", Ann Math Stat, 9, pp.60~62 (1938)
- Einmahl JHJ, "An M-estimator of spatial tail dependence", J Roy Stat Soc B, 78, pp.275~298 (2016)