Analyzing memory effects of complex systems from time series

Abstract

A numerical algorithm is presented in order to determine all coefficients of the Mori-Zwanzig equation from a given finite time series. The algorithm is applicable to observables of arbitrary complex systems. Meteorological and financial systems are investigated. By analyzing directional variables and amplitudes we are able to observe and discuss memory effects on different time scales. We show that analyzing the memory kernel provides important insights into the dynamics of a complex system.