ANTICORRELATIONS AND SUBDIFFUSION IN FINANCIAL SYSTEMS

Abstract

Statistical dynamics of financial systems is investigated, based on a model of a randomly coupled equation system driven by a stochastic Langevin force. It is found that in a stable regime the noise power spectrum of the system is 1/f-like: ∝ ω- 3/2 (where ω is the frequency), that the autocorrelation function of the increments of the variables (returns of prices) is negative and follows the power law: ∝ - τ- 3/2 (where τ is the delay), and that the stochastic drift of the variables (prices, exchange rates) is subdiffusive: ∝ tH (where t is the time, H ≈ 1/4 is the Hurst, or self-similarity, exponent). These dependencies correspond to those calculated from historical $/EURO exchange rates.