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.
Highlights
Many stock market analysts rely on various technical indicators calculated for individual stocks
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 and long enough length of time series
The method was first proposed and applied on stock prices by Plerou, et al [1,2] on daily close prices of American stocks and Laloux, et al [3] applied on daily close prices of Japanese stocks by Aoyama et al This method uses a result of random matrix theory (RMT) [4,5,6] on the principal component analysis of the cross correlation matrix of pairs of independent time series
Summary
Many stock market analysts rely on various technical indicators calculated for individual stocks. The average size of the relevant time scales are not very long, typically shown by the auto-correlation function of the price time series vanish after a few ticks. This fact makes the prediction of future market situation difficult. Due to the higher frequency of data points, we can compare the results of different years and describe the historical change of the market in the scenario of this new method of principal component analysis based on RMT spectrum.
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