Statistical properties of stock market eigensignals

By using the correlation matrix approach, we decompose the evolution of a set of the 100 largest American companies into the components (portfolios) defined by the eigenvectors of the correlation matrix. Among the results, we show that a number of the non-random components exceeds the previous estimates based on much shorter time series of daily returns. This indicates that for short signals the bulk of random eigenvalues defined by Random Matrix Theory can comprise also a significant amount of information. We also show that the components corresponding to a few largest eigenvalues and describing the most collective part of the market evolution reveal strong nonlinear correlation structure in contrast to the other components. All the components are multifractal. Moreover, by using a modified definition of the correlation matrix, we are able to decompose the daily pattern of the German DAX30 index into components which can characterize the recurrent events occurring at precise moments of a trading day.