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

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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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


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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?


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Scaling in Zipf plots

Stock market Currency Earthquakes

Length return

interval for a given

threshold q

Ranking in

decreasing length

Scaling function


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Scaling in distributions

Stock market Currency Earthquakes

probability

distribution to have

a return interval

for a given q

Yen-Dollar

Japan

IBM

Scaling function


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Memory in the records

Conditional probability

for having a return interval

after

for


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Memory in the distributions

Clustering of extreme events

Stock market Currency

Earthquakes

Scaling function


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Memory in the averages

Stock market Currency

mean conditional

return interval

Earthquakes


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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.


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  • 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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