Potential force observed in market dynamics

Abstract

As a model of market price, we introduce a new type of random walk in a moving potential, which is approximated by a quadratic function with its center given by the moving average of its own trace. The properties of resulting random walks are similar to those of ordinary random walks for large time scales; however, their short-time properties are approximated by abnormal diffusion with nontrivial exponents. A new data-analysis method based on this model enables us to observe temporal changes of potential forces from high-precision market data directly.