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Long term memory in extreme returns of financial time series

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  • Muchnik, Lev
  • Bunde, Armin
  • Havlin, Shlomo

Abstract

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.

Suggested Citation

  • Muchnik, Lev & Bunde, Armin & Havlin, Shlomo, 2009. "Long term memory in extreme returns of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4145-4150.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:19:p:4145-4150
    DOI: 10.1016/j.physa.2009.05.046
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