Open Access

Illia Horenko, Frank Noe, Carsten Hartmann, Christof Schütte

• he generalized Langevin equation is useful for modeling a wide range of physical processes. Unfortunately its parameters, especially the memory function, are difficult to determine for nontrivial processes. In this paper, relations between a time-discrete generalized Langevin model and discrete multivariate autoregressive (AR) or autoregressive moving average models (ARMA) are established. This allows a wide range of discrete linear methods known from time series analysis to be applied. In particular, the determination of the memory function {\it via} the order of the respective AR or ARMA model is addressed. The method is illustrated on a one-dimensional test system and subsequently applied to the molecular dynamics of a biomolecule which exhibits an interesting relationship between the solvent method used, the molecular conformation and the depth of the memory.