From turbulence to financial time series

Abstract

We develop a framework especially suited to the autocorrelation properties observed in financial times series, by borrowing from the physical picture of turbulence. The success of our approach as applied to high frequency foreign exchange data is demonstrated by the overlap of the curves in Figure (1), since we are able to provide an analytical derivation of the relative sizes of the quantities depicted. These quantities include departures from Gaussian probability density functions and various two and three-point autocorrelation functions.