Reconciling econophysics with macroeconomic theory

Recent studies have found that many financial market time series scale as f ractals. Much of the methodology is explicitly derived from physics, so muc h so that the field has been called econophysics. Since fractals have been identified primarily in the physical sciences, there has been a tendency in this literature to assume that the mechanisms leading to fractality in fin ancial markets are analogous, The parallels between physics and economics c annot be carried too far, however, since the structural equations used in e conometric models do not posit the same causal mechanisms. The widely used cascade model in physics does not operate in economics. For instance, excha nge rates are not determined by multiplicative cascades, but rather by diff erentials in rates of return and relative prices. Moreover, the property of long-term scaling symmetries, which has been found in some physical proces ses, runs counter to economic theory. Economic processes are turbulent at s hort horizons, but theory states that at longer horizons they should conver ge to an equilibrium state. Nevertheless, the equations normally used to pr edict exchange rates do imply that currencies will show fractal properties, at least at near-term horizons. These equations do not generate strong sca ling symmetries, but rather only weaker scaling symmetries over shorter tim e intervals. Empirical tests find that both exchange rates and the interest rate differentials that cause them are fractal: they show non-integer dime nsionality. The degree of fractality, measured by the codimension, diminish es as a function of the time scale. At long horizons, financial markets mov e toward a non-fractal state. The probability distribution also shifts as t he time scale increases. (C) 2000 Elsevier Science B.V. All rights reserved .