SCALING BEHAVIOR IN THE DYNAMICS OF AN ECONOMIC INDEX

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 criticality(1) and turbulence(2,3). Such systems tend to exhibit spatial and temporal sealing 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 systems-especially especially when the economic system is one subject to precise rules, as is the case in financial market(6-8). Specifically, we show that the scaling of the probability distribution of a particular economic index-the Standard and 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 Levy 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 Levy 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.