Cross Correlation of Intra-day Stock Prices in Comparison to Random Matrix Theory

Mieko Tanaka-Yamawaki

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DOI: 10.4236/iim.2011.33008                

Abstract

We propose and apply a new algorithm of principal component analysis which is suitable for a large sized, highly random time series data, such as a set of stock prices in a stock market. This algorithm utilizes the fact that the major part of the time series is random, and compare the eigenvalue spectrum of cross correlation matrix of a large set of random time series, to the spectrum derived by the random matrix theory (RMT) at the limit of large dimension (the number of independent time series) and long enough length of time series. We test this algorithm on the real tick data of American stocks at different years between 1994 and 2002 and show that the extracted principal components indeed reflects the change of leading stock sectors during this period.

Keywords

Principal Component, Random Matrix Theory, Cross Correlation, Eigenvalues, Stock Market

Conflicts of Interest

The authors declare no conflicts of interest.

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