Scaling behaviour in the dynamics of an economic index
Abstract
THE largescale dynamical properties of some physical systems depend on the dynamical evolution of a large number of nonlinearly coupled subsystems. Examples include systems that exhibit selforganized criticality^{1} and turbulence^{2,3}. Such systems tend to exhibit spatial and temporal scaling behaviour power law behaviour of a particular observable. Scaling is found in a wide range of systems, from geophysical^{4} to biological^{5}. Here we explore the possibility that scaling phenomena occur in economic systemsáespecially when the economic system is one subject to precise rules, as is the case in financial markets^{6 8}. Specifically, we show that the scaling of the probability distribution of a particular economic index the Standard & Poor's 500 can be described by a nongaussian process with dynamics that, for the central part of the distribution, correspond to that predicted for a Lévy stable process^{9 11}. Scaling behaviour is observed for time intervals spanning three orders of magnitude, from 1,000 min to 1 min, the latter being close to the minimum time necessary to perform a trading transaction in a financial market. In the tails of the distribution the falloff deviates from that for a Lévy stable process and is approximately exponential, ensuring that (as one would expect for a price difference distribution) the variance of the distribution is finite. The scaling exponent is remarkably constant over the sixyear period (198489) of our data. This dynamical behaviour of the economic index should provide a framework within which to develop economic models.
 Publication:

Nature
 Pub Date:
 July 1995
 DOI:
 10.1038/376046a0
 Bibcode:
 1995Natur.376...46M