Random Matrix Approach to Correlation Matrix of Financial Data (Mexican Stock Market Case)

Abstract

The main purpose of this work is to reproduce the method used for U.S. market which consists in the approach of random matrices to crossed correlation matrices built with financial data taken from a Mexican stock market database. First we built a cross correlation empirical matrix with these financial data. Eigenvalue spectrum was obtained from this matrix. We made the same spectrum analysis for a random matrix, and finally we compared both eigenvalue sets, and we tried to set up a hypothesis of how risk was related to this random matrix-correlation matrix approach. We used financial data over a period of six months and time series where made upon three hours measures for crossed correlation matrix.

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González, J. and Torres, A. (2015) Random Matrix Approach to Correlation Matrix of Financial Data (Mexican Stock Market Case). Modern Economy, 6, 1033-1042. doi: 10.4236/me.2015.69099.

Conflicts of Interest

The authors declare no conflicts of interest.

 [1] Marchenko, V.A. and Pastur, L.A. (1967) Distribution of Eigenvalues for Some Sets of Random Matrices. Sbornik: Mathematics, 1, 457-483. [2] Landau, L.D. and Lifshitz, E.M. (2009) Quantum Mechanics (Non-Relativistic Theory). Theoretical Physics. [3] Plerou, V., Gopikrishnan, P., Rosenow, B., Nunes, L.A., Guhr, T. and Stanley, H.E. (2002) Random Matrix Approach to Cross Correlations in Financial Data. Physical Review, 65, 066126-1-18. [4] Bolsa Mexicana de Valores [en línea]. México. Data Available in: http://www.bmv.com.mx/. [5] Medina, L.M. and Mancilla, R. (2008) Teoría de matrices aleatorias y su correlación con las series financieras: El caso de la Bolsa Mexicana de Valores. Journal of Management, Finance and Economics, 2, 125-135. [6] Acciones del Mercado Mexicano de Valores [en línea]. Mexico. Database Was Available in: http://www.economia.terra.com.mx/mercados/acciones. [7] Antonio Alatorre[Online]. Mexico. Database Available in: http://alatorre.rus.tl/downloads.html [8] Gutzwiller, M. (1990) Chaos in Classical and Quantum Mechanics. Springer-Verlag, New York. [9] Johnstone, I. (1983) Wishart, Wigner and Weather—Eigenvalues in Statistics and Beyond. Public Lecture at Chinese University of Hong Kong (T Y Wong Hall, 5/F, Sin-Hang Engineering Building), at 4:30 p.m. [10] Pastur, L. and Shcherbina, M. (1997) Universality of the Local Eigenvalue Statistics for a Class of Unitary Invariant Random Matrix Ensembles. Journal of Statistical Physics. http://arxiv.org/abs/0906.0510