2006/09/22 by Kevin E. Bassler, Joseph L. McCauley, Gemunu H. Gunaratne · 4 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Chaos control and synchronization #Complex Systems and Time Series Analysis #Financial Risk and Volatility Modeling #cond-mat.stat-mech #physics.data-an #physics.soc-ph #q-fin.ST
paper · pdf · doi:10.1073/pnas.0708664104
12 pages, 4 figures
arxiv created 2006/09/22 · openalex publication_date 2007/10/23 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Fat-tailed distributions have been reported in fluctuations of financial markets for more than a decade. Sliding interval techniques used in these studies implicitly assume that the underlying stochastic process has stationary increments. Through an analysis of intraday increments, we explicitly show that this assumption is invalid for the Euro-Dollar exchange rate. We find several time intervals during the day where the standard deviation of increments exhibits power law behavior in time. Stochastic dynamics during these intervals is shown to be given by diffusion processes with a diffusion coefficient that depends on time and the exchange rate. We introduce methods to evaluate the dynamical scaling index and the scaling function empirically. In general, the scaling index is significantly smaller than previously reported values close to 0.5. We show how the latter as well as apparent fat-tailed distributions can occur only as artifacts of the sliding interval analysis.