Local Scaling Analysis with Continuous DFA in High Frequency Financial Time Series

M. Chorowskia, Z.R. Struzika, b, c aFaculty of Physics, University of Warsaw, L. Pasteura 5, PL-02093 Warsaw, Poland bAdvanced Center for Computing and Communication, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan cGraduate School of Education, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

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The crucial question every investor has to answer before buying stock is: what is the risk associated with it? In this work, we applied the Continuous Detrended Fluctuation Analysis (CDFA) to uncover the point-wise Hölder exponent of the time series at various time scales. The Hölder exponent is a time-dependent measure of the autocorrelation of the variability in data, and it can be used to measure the market risk. CDFA is an extension of the popular Detrended Fluctuation Analysis (DFA) method, but - contrary to DFA - it allows for estimating the Hölder exponent locally. We used this method to study the two-minute frequency data of the U.S. S&P 500 index from 1984 to 1995. We found that the value of the exponent increases as lower resolution data was used, which means the financial time series appear more predictable at higher scales than at lower scales. Moreover, we found that correlations between the Hölder exponent and the log returns and absolute log returns are scale-dependent. That means that the CDFA method could potentially be used in the future to identify time scales at which the series are the most predictable which can have practical applications.

DOI:10.12693/APhysPolA.139.407 topics: econophysics, financial time series, Hölder exponent, detrended fluctuation