Toward a scenario with complementary stochastic and deterministic information in financial fluctuations

We present the results of our analysis of time series for a collection of 345 stocks listed in S&P 500, to show that integrated information on collective fluctuations in financial data can be revealed quantitatively on two aspects, focusing on either the stochastic or the deterministic content of the data. The latter is obtained by relating the fluctuations in high frequency data of one-day moving averages (HF1MA) for the prices of individual stocks analogously to the displacements for Brownian motion for the tracer particles. It has been shown in a previous study of data for each month over the years 1996-1999 [11], that the kinetic parameters carry effectively the market-specific information. In an attempt to extend such a many-particle scenario, we pay attention in this study to the stock-stock cross correlations and decompose the fluctuations into the Karhunan-Loe`ve expansions, to find the general features of the collective modes in their time-wise as well as the stock-wise components, comparing the results for the time series of original prices and those of HF1MA. We found robust patterns of time-wise correlations in the eigenmodes, which may be analyzed further to find market-specific information.