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.
Highlights
Random Matrix Theory has been one of those mathematical discoveries or inventions from physicists due to their need to solve problems for physics
We do not use the classic chaos concept known from physics for which chaos or chaotic systems are understood as non-integrable dynamical systems
Applications on financial engineering have been made of in this article. Just as it was comment at the abstract, we took a database of financial data of Mexican stock market taken from [4]. (Details of database are better explained in Subsection 3.) We built time series for these data on purpose to have a cross correlation matrix that we called “empirical matrix” in order to analyse its eigenvalue spectrum
Summary
Random Matrix Theory has been one of those mathematical discoveries or inventions from physicists due to their need to solve problems for physics. The main idea to use properly this tool would be taking data from a complex system, building a correlation matrix with these data by time series method for real entries and comparing its spectrum with the spectrum of a random matrix. (Details of database are better explained in Subsection 3.) We built time series for these data on purpose to have a cross correlation matrix that we called “empirical matrix” in order to analyse its eigenvalue spectrum. We plotted these eigenvalue spectrum and we let it ready to compare it with random matrix one as long as we found a random matrix of the same dimension with their respective eigenvalues. One can find whole data information, time series, plots of time series and correlation matrix entries from a special package of [6]
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