TY - JOUR
T1 - Scaling and correlation in financial time series
AU - Gopikrishnan, P.
AU - Plerou, V.
AU - Liu, Y.
AU - Amaral, L. A N
AU - Gabaix, X.
AU - Stanley, H. E.
PY - 2000/12/1
Y1 - 2000/12/1
N2 - 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 Levy 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.
AB - 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 Levy 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.
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U2 - 10.1016/S0378-4371(00)00375-7
DO - 10.1016/S0378-4371(00)00375-7
M3 - Article
AN - SCOPUS:0034502120
VL - 287
SP - 362
EP - 373
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
SN - 0378-4371
IS - 3-4
ER -