Extracting Principal Components from Pseudo-random Data by Using Random Matrix Theory

Abstract

We develop a methodology to grasp temporal trend in a stock market that changes year to year, or sometimes within a year depending on numerous factors. For this purpose, we employ a new algorithm to extract significant principal components in a large dimensional space of stock time series. The key point of this method lies in the randomness and complexity of the stock time series. Here we extract significant principal components by picking a few distinctly large eigenvalues of cross correlation matrix of stock pairs in comparison to the known spectrum of corresponding random matrix derived in the random matrix theory (RMT). The criterion to separate signal from noise is the maximum value of the theoretical spectrum of We test the method using 1 hour data extracted from NYSE-TAQ database of tickwise stock prices, as well as daily close price and show that the result correctly reflect the actual trend of the market.