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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

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Presentation Transcript
slide1
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

slide2
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?
slide3
Scaling in Zipf plots

Stock market Currency Earthquakes

Length return

interval for a given

threshold q

Ranking in

decreasing length

Scaling function

slide4
Scaling in distributions

Stock market Currency Earthquakes

probability

distribution to have

a return interval

for a given q

Yen-Dollar

Japan

IBM

Scaling function

slide5
Memory in the records

Conditional probability

for having a return interval

after

for

slide6
Memory in the distributions

Clustering of extreme events

Stock market Currency

Earthquakes

Scaling function

slide7
Memory in the averages

Stock market Currency

mean conditional

return interval

Earthquakes

slide8
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.
slide9
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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