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Scaling and correlation in financial time series

Author

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  • Gopikrishnan, P
  • Plerou, V
  • Liu, Y
  • Amaral, L.A.N
  • Gabaix, X
  • Stanley, H.E

Abstract

We discuss the results of three recent phenomenological studies focussed on understanding the distinctive statistical properties of financial time series – (i) The probability distribution of stock price fluctuations: Stock price fluctuations occur in all magnitudes, in analogy to earthquakes – from tiny fluctuations to very drastic events, such as the crash of 19 October 1987, sometimes referred to as “Black Monday”. The distribution of price fluctuations decays with a power-law tail well outside the Lévy stable regime and describes fluctuations that differ by as much as 8 orders of magnitude. In addition, this distribution preserves its functional form for fluctuations on time scales that differ by 3 orders of magnitude, from 1 min up to approximately 10 days. (ii) Correlations in financial time series: While price fluctuations themselves have rapidly decaying correlations, the magnitude of fluctuations measured by either the absolute value or the square of the price fluctuations has correlations that decay as a power-law, persisting for several months. (iii) Volatility and trading activity: We quantify the relation between trading activity – measured by the number of transactions NΔt – and the price change GΔt for a given stock, over a time interval [t,t+Δt]. We find that NΔt displays long-range power-law correlations in time, which leads to the interpretation that the long-range correlations previously found for |GΔt| are connected to those of NΔt.

Suggested Citation

  • Gopikrishnan, P & Plerou, V & Liu, Y & Amaral, L.A.N & Gabaix, X & Stanley, H.E, 2000. "Scaling and correlation in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 362-373.
    • Handle: RePEc:eee:phsmap:v:287:y:2000:i:3:p:362-373
    DOI: 10.1016/S0378-4371(00)00375-7
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    References listed on IDEAS

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    1. J. Doyne Farmer, 2000. "Physicists Attempt To Scale The Ivory Towers Of Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 311-333.
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