From short to fat tails in financial markets: A unified description

摘要

In complex systems such as turbulent flows and financial markets, thedynamics in long and short time-lags, signaled by Gaussian and fat-tailedstatistics, respectively, calls for a unified description. To address thisissue we analyze a real dataset, namely, price fluctuations, in a wide range oftemporal scales to embrace both regimes. By means of Kramers-Moyal (KM)coefficients evaluated from empirical time series, we obtain the evolutionequation for the probability density function (PDF) of price returns. We alsopresent consistent asymptotic solutions for the timescale dependent equationthat emerges from the empirical analysis. From these solutions, newrelationships connecting PDF characteristics, such as tail exponents, toparameters of KM coefficients arise. The results reveal a dynamical path thatleads from Gaussian to fat-tailed statistics, furnishing insights on othercomplex systems where akin crossover is observed.