文档介绍：Physica A 287 (2000) 362–373
ate/physa
Scaling and correlation in ÿnancial time series
P. Gopikrishnana; ∗, V. Pleroua , , . Amarala ,
X. Gabaixb;c , . Stanleya
aCenter for Polymer Studies and Department of Physics Boston University, Boston, MA 02215, USA
bDepartment of Economics, Massachusetts Institute of Technology, Cambridge, MA 02142, USA
cDepartment of Economics, The University of Chicago, Chicago, IL 60637, USA
Received 13 May 2000
Abstract
We discuss the results of three recent phenomenological studies focussed on understanding the
distinctive statistical properties of ÿnancial time series –(i) The probability distribution of stock
price
uctuations: Stock price
uctuations occur in all magnitudes, in analogy to earthquakes –
from tiny
uctuations to very drastic events, such as the crash of 19 October 1987, sometimes
referred to as “Black Monday”. The distribution of price
uctuations decays with a power-law
tail well outside the LÃevy stable regime and describes
uctuations that di er by as much as 8
orders of magnitude. In addition, this distribution preserves its functional form for
uctuations
on time scales that di er by 3 orders of magnitude, from 1 min up to approximately 10 days.
(ii) Correlations in ÿnancial time series: While price
uctuations themselves have rapidly de-
caying correlations, the magnitude of
uctuations measured by either the absolute value or the
square of the price
uctuations 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 Nt – and the price change Gt for a given stock, over
a time interval [t; t +t]. We ÿnd that Nt displays long-range power-law correlations in time,
which leads to the interpretation that the long-range correlations previously found for |Gt | are
connected to those of Nt .
c 2000 Elsevier Science . A