Inverse Fractal Statistics in Turbulence and Finance

Abstract

We consider inverse statistics in turbulence and financial data. By inverse statistics, also sometimes called exit time statistics, we "turn" the variables around such that the fluctuating variable becomes the fixed variable, while the fixed variable becomes fluctuating. In that sense we can probe distinct regimes of the data sets. In the case of turbulence, we obtain a new set of (multi)-scaling exponents which monitor the dissipation regime. In the case of economics, we obtain a distribution of waiting times needed to achieve a predefined level of return. Such a distribution typically goes through a maximum at a time called the optimal investment horizon[Formula: see text], since this defines the most likely waiting time for obtaining a given return ρ. By considering equal positive and negative levels of return, we report on a quantitative gain-loss asymmetry most pronounced for short horizons.