Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient

2013 ◽  
Vol 392 (17) ◽  
pp. 3715-3730 ◽  
Author(s):  
Gang-Jin Wang ◽  
Chi Xie ◽  
Shou Chen ◽  
Jiao-Jiao Yang ◽  
Ming-Yan Yang
Keyword(s):  
Stock Market ◽  
Correlation Coefficient ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Cross Correlation ◽  
Matrix Theory ◽  
Theory Analysis ◽  
Pearson’S Correlation Coefficient ◽  
The Us ◽  
Cross Correlations

scholarly journals ECONOPHYSICS: WHAT CAN PHYSICISTS CONTRIBUTE TO ECONOMICS?

2000 ◽  
Vol 03 (03) ◽  
pp. 335-346 ◽  
Author(s):  
H. EUGENE STANLEY ◽  
LUÍS A. NUNES AMARAL ◽  
PARAMESWARAN GOPIKRISHNAN ◽  
YANHUI LIU ◽  
VASILIKI PLEROU ◽  
...  
Keyword(s):  
Time Series ◽  
Power Law ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Correlation Matrix ◽  
Cross Correlation ◽  
Matrix Theory ◽  
Financial Time Series ◽  
Price Fluctuations ◽  
Financial Time

In recent years, a considerable number of physicists have started applying physics concepts and methods to understand economic phenomena. The term "Econophysics" is sometimes used to describe this work. Economic fluctuations can have many repercussions, and understanding fluctuations is a topic that many physicists have contributed to in recent years. Further, economic systems are examples of complex interacting systems for which a huge amount of data exist and it is possible that the experience gained by physicists in studying fluctuations in physical systems might yield new results in economics. Much recent work in econophysics is focused on understanding the peculiar statistical properties of price fluctuations in financial time series. In this talk, we discuss three recent results. The first result concerns the probability distribution of stock price fluctuations. This distribution decreases with increasing fluctuations with a power-law tail well outside the Lévy stable regime and describes fluctuations that differ by as much as 8 orders of magnitude. Further, this nonstable distribution preserves its functional form for fluctuations on time scales that differ by 3 orders of magnitude, from 1 min up to approximately 10 days. The second result concerns the accurate quantification of volatility correlations in financial time series. While price fluctuations themselves have rapidly decaying correlations, the volatility estimated by using either the absolute value or the square of the price fluctuations has correlations that decay as a power-law and persist for several months. The third result bears on the application of random matrix theory to understand the correlations among price fluctuations of any two different stocks. We compare the statistics of the cross-correlation matrix constructed from price fluctuations of the leading 1000 stocks and a matrix with independent random elements, i.e., a random matrix. Contrary to first expectations, we find little or no deviation from the universal predictions of random matrix theory for all but a few of the largest eigenvalues of the cross-correlation matrix.

APPLICATION OF RANDOM MATRIX THEORY TO STUDY CROSS-CORRELATIONS OF STOCK PRICES

2000 ◽  
Vol 03 (03) ◽  
pp. 399-403 ◽  
Author(s):  
BERND ROSENOW ◽  
VASILIKI PLEROU ◽  
PARAMESWARAN GOPIKRISHNAN ◽  
LUÍS A. NUNES AMARAL ◽  
H. EUGENE STANLEY
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Stock Prices ◽  
Matrix Theory ◽  
Localization Theory ◽  
Largest Eigenvalues ◽  
Cross Correlations ◽  
Universal Properties ◽  
Matrix Formula ◽  
Gaussian Orthogonal Ensemble

We address the question of how to precisely identify correlated behavior between different firms in the economy by applying methods of random matrix theory (RMT). Specifically, we use methods of random matrix theory to analyze the cross-correlation matrix [Formula: see text] of price changes of the largest 1000 US stocks for the 2-year period 1994–1995. We find that the statistics of most of the eigenvalues in the spectrum of [Formula: see text] agree with the predictions of random matrix theory, but there are deviations for a few of the largest eigenvalues. To prove that the rest of the eigenvalues are genuinely random, we test for universal properties such as eigenvalue spacings and eigenvalue correlations. We demonstrate that [Formula: see text] shares universal properties with the Gaussian orthogonal ensemble of random matrices. In addition, we quantify the number of significant participants, that is companies, of the eigenvectors using the inverse participation ratio, and find eigenvectors with large inverse participation ratios at both edges of the eigenvalue spectrum — a situation reminiscent of results in localization theory.

Random Matrix Theory Applied to Portfolio Optimization in Japanese Stock Market

2006 ◽  
pp. 286-290
Author(s):  
Masashi Egi ◽  
Takashi Matsushita ◽  
Seiji Futatsugi ◽  
Keizaburo Murakami
Keyword(s):  
Stock Market ◽  
Portfolio Optimization ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Japanese Stock Market
Sign in / Sign up

Export Citation Format

Share Document