https://doi.org/10.1140/epjb/e2006-00356-9
Statistical regularities in the return intervals of volatility
1
Center for Polymer Studies and Department of Physics, Boston University, Boston, MA, 02215, USA
2
Institut für Theoretische Physik, Universität zu Köln, 50937 Köln, Germany
3
Department of Environmental Sciences, Tokyo University of Information Sciences, Chiba, 265-8501, Japan
4
Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan, 52900, Israel
Corresponding author: a fzwang@bu.edu
Received:
30
May
2006
Revised:
28
July
2006
Published online:
4
October
2006
We discuss recent results concerning statistical regularities in the return intervals of volatility in financial markets. In particular, we show how the analysis of volatility return intervals, defined as the time between two volatilities larger than a given threshold, can help to get a better understanding of the behavior of financial time series. We find scaling in the distribution of return intervals for thresholds ranging over a factor of 25, from 0.6 to 15 standard deviations, and also for various time windows from one minute up to 390 min (an entire trading day). Moreover, these results are universal for different stocks, commodities, interest rates as well as currencies. We also analyze the memory in the return intervals which relates to the memory in the volatility and find two scaling regimes, ℓ<ℓ* with α1=0.64±0.02 and ℓ> ℓ* with α2=0.92±0.04; these exponent values are similar to results of Liu et al. for the volatility. As an application, we use the scaling and memory properties of the return intervals to suggest a possibly useful method for estimating risk.
PACS: 89.65.Gh – Economics; econophysics, financial markets, business and management / 05.45.Tp – Time series analysis / 89.75.Da – Systems obeying scaling laws
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006