Long term memory in extreme returns of financial time series

Lev Muchnik, Armin Bunde, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


It is well known that while daily price returns of financial markets are uncorrelated, their absolute values ('volatility') are long-term correlated. Here we provide evidence that certain subsequences of the returns themselves also exhibit long-term memory. These subsequences consist of maxima (or minima) of returns in consecutive time windows of R days. Our analysis shows that for both stocks and currency exchange rates, long-term correlations are significant for R ≥ 4. We argue that this long-term memory which is similar to that observed in volatility clustering sheds further insight on price dynamics that might be used for risk estimation.

Original languageEnglish
Pages (from-to)4145-4150
Number of pages6
JournalPhysica A: Statistical Mechanics and its Applications
Issue number19
StatePublished - 1 Oct 2009


  • Econophysics
  • Extreme values
  • Long-term correlation
  • Long-term memory
  • Volatility


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