Effect of changing data size on eigenvalues in the Korean and Japanese stock markets

In this study, we attempted to determine how eigenvalues change, according to random matrix theory (RMT), in stock market data as the number of stocks comprising the correlation matrix changes. Specifically, we tested for changes in the eigenvalue properties as a function of the number and type of stocks in the correlation matrix. We determined that the value of the eigenvalue increases in proportion with the number of stocks. Furthermore, we noted that the largest eigenvalue maintains its identical properties, regardless of the number and type, whereas other eigenvalues evidence different features.

[1]  J. Bouchaud,et al.  Noise Dressing of Financial Correlation Matrices , 1998, cond-mat/9810255.

[2]  Stephen J. Brown.  The Number of Factors in Security Returns , 1989 .

[3]  Hawoong Jeong,et al.  Systematic analysis of group identification in stock markets. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  E. Fama,et al.  Common risk factors in the returns on stocks and bonds , 1993 .

[5]  H. Kaiser.  The varimax criterion for analytic rotation in factor analysis , 1958 .

[6]  F. Black,et al.  The Capital Asset Pricing Model: Some Empirical Tests , 2006 .

[7]  Gregory Connor,et al.  A Test for the Number of Factors in an Approximate Factor Model , 1993 .

[8]  G. Oh,et al.  Statistical Investigation of Connected Structures of Stock Networks in Financial Time Series , 2007, 0709.2200.

[9]  M. Oshikawa,et al.  Random matrix theory analysis of cross correlations in financial markets. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Charles Trzcinka,et al.  On the Number of Factors in the Arbitrage Pricing Model , 1986 .

[11]  B. King.  Market and Industry Factors in Stock Price Behavior , 1966 .

[12]  V. Plerou,et al.  Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series , 1999, cond-mat/9902283.

[13]  M. Rothschild,et al.  Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets , 1982 .

[14]  Anirvan M. Sengupta,et al.  Distributions of singular values for some random matrices. , 1997, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  S. Ross.  The arbitrage theory of capital asset pricing , 1976 .

[16]  H. Harman.  Modern factor analysis , 1961 .

[17]  V. Plerou,et al.  Random matrix approach to cross correlations in financial data. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Gabjin Oh,et al.  Deterministic factors of stock networks based on cross-correlation in financial market , 2007, 0705.0076.