Asymmetric Finite-Range Persistence in Time Series Generated by the Modified Discrete Langevin Model

The concept of asymmetric persistence in time series was proposed and an appropriate stochastic Langevin-type model was presented. The influence of this particular form of memory on the behavior of the generated time series was examined. It has been shown that asymmetry causes a significant distortion of the effect of drift forces and has a weaker impact on stochastic diffusion forces. Due to this, current known methods for reconstructing the Langevin-type model fail. The results of this work may help in deriving a new reconstruction method.