Reconciling econophysics with macroeconomic theory

Recent studies have found that many financial market time series scale as fractals. Much of the methodology is explicitly derived from physics, so much 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 financial markets are analogous. The parallels between physics and economics cannot be carried too far, however, since the structural equations used in econometric models do not posit the same causal mechanisms. The widely used cascade model in physics does not operate in economics. For instance, exchange rates are not determined by multiplicative cascades, but rather by differentials in rates of return and relative prices. Moreover, the property of long-term scaling symmetries, which has been found in some physical processes, runs counter to economic theory. Economic processes are turbulent at short horizons, but theory states that at longer horizons they should converge to an equilibrium state. Nevertheless, the equations normally used to predict exchange rates do imply that currencies will show fractal properties, at least at near-term horizons. These equations do not generate strong scaling symmetries, but rather only weaker scaling symmetries over shorter time intervals. Empirical tests find that both exchange rates and the interest rate differentials that cause them are fractal: they show non-integer dimensionality. The degree of fractality, measured by the codimension, diminishes as a function of the time scale. At long horizons, financial markets move toward a non-fractal state. The probability distribution also shifts as the time scale increases.