Statistical regularities in the return intervals of volatility |
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| Authors: | F Wang P Weber K Yamasaki S Havlin H E Stanley |
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| Institution: | 1.Center for Polymer Studies and Department of Physics,Boston University,Boston,USA;2.Institut für Theoretische Physik, Universit?t zu K?ln,K?ln,Germany;3.Department of Environmental Sciences,Tokyo University of Information Sciences,Chiba,Japan;4.Minerva Center and Department of Physics,Bar-Ilan University,Ramat-Gan,Israel |
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| Abstract: | 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. |
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| Keywords: | 89 65 Gh Economics econophysics financial markets business and management 05 45 Tp Time series analysis 89 75 Da Systems obeying scaling laws |
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