Scaling behaviour in the dynamics of an economic index

Abstract

THE large-scale dynamical properties of some physical systems depend on the dynamical evolution of a large number of nonlinearly coupled subsystems. Examples include systems that exhibit self-organized criticality¹ 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 geophysical⁴ to biological⁵. Here we explore the possibility that scaling phenomena occur in economic systemsá-especially 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 non-gaussian 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 fall-off 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 six-year period (1984-89) of our data. This dynamical behaviour of the economic index should provide a framework within which to develop economic models.