Scaling and memory in volatility return intervals in financial markets

Kazuko Yamasaki, Lev Muchnik, Shlomo Havlin, Armin Bunde, H. Eugene Stanley

Research output: Contribution to journalArticlepeer-review

221 Scopus citations


For both stock and currency markets, we study the return intervals τ between the daily volatilities of the price changes that are above a certain threshold q. We find that the distribution function Pq(τ) scales with the mean return interval τ̄ as Pq(τ) = τ̄-1f(τ/τ̄). The scaling function f(x) is similar in form for all seven stocks and for all seven currency databases analyzed, and f(x) is consistent with a power-law form, f(x) ∼ x with γ ≈ 2. We also quantify how the conditional distribution Pq(τ/τ0) depends on the previous return interval TQ and find that small (or large) return intervals are more likely to be followed by small (or large) return intervals. This "clustering" of the volatility return intervals is a previously unrecognized phenomenon that we relate to the long-term correlations known to be present in the volatility.

Original languageEnglish
Pages (from-to)9424-9428
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number26
StatePublished - 28 Jun 2005


  • Econophysics
  • Extreme values
  • Fluctuations
  • Long-term correlations
  • Long-term memory


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