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Scaling and Memory in Stock Market and Currency Variations: Similarities to Earthquakes

Scaling and Memory in Stock Market and Currency Variations: Similarities to Earthquakes Shlomo Havlin Bar-Ilan, Israel in collaboration with Kazuko Yamasaki Tokyo, Japan Valerie Livina, Sergey Tuzov, Lev Muchnik Bar-Ilan, Israel Armin Bunde Giessen, Germany H. Eugene Stanley

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Scaling and Memory in Stock Market and Currency Variations: Similarities to Earthquakes

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  1. Scaling and Memory in Stock Market and Currency Variations: Similarities to Earthquakes Shlomo Havlin Bar-Ilan, Israel in collaboration with Kazuko Yamasaki Tokyo, Japan Valerie Livina, Sergey Tuzov, Lev Muchnik Bar-Ilan, Israel Armin Bunde Giessen, Germany H. Eugene Stanley Boston, USA

  2. Return intervals Stock market data Currency series Earthquakes Normalized absolute return Challenges: • (a) Are there scaling laws in return intervals? • (b) Is there memory in the records of return • intervals? • (c) Are there similarities between economy and • earthquakes? • (d) How can we improve forecast of extreme events?

  3. Scaling in Zipf plots Stock market Currency Earthquakes Length return interval for a given threshold q Ranking in decreasing length Scaling function

  4. Scaling in distributions Stock market Currency Earthquakes probability distribution to have a return interval for a given q Yen-Dollar Japan IBM Scaling function

  5. Memory in the records Conditional probability for having a return interval after for

  6. Memory in the distributions Clustering of extreme events Stock market Currency Earthquakes Scaling function

  7. Memory in the averages Stock market Currency mean conditional return interval Earthquakes

  8. Summary • Scaling of return intervals Well approximated by single scaled function. • Strong effect of memory • Origin: long-term correlations in the volatilities. • Strong similarity in both scaling (for different q) and memory to earthquakes. • Application: improving risk assessment.

  9. Bibliography • V. Livina, S. Tuzov, S. Havlin, A.Bunde, Recurrence • intervals between earthquakes strongly depend on • history, preprint physics/0410274 (Physica A, in press). • Bunde, J. Eichner, J. Kantelhardt, S. Havlin, Long- • term memory: natural mechanism for the clustering of • extreme events and anomalous residual times in climate • Records (PRL, to appear). • K. Yamasaki, S. Havlin, A. Bunde, H. E. Stanley, Scaling • and memory in volatility return intervals in stock markets • (to appear)

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