Effect of nonlinearity and persistence on multiscale irreversibility, non-stationarity, and complexity of time series-Case of data generated by the modified Langevin model

Stochastic models of a time series can take the form of a nonlinear equation and have a built-in memory mechanism. Generated time series can be characterized by measures of certain features, e.g., non-stationarity, irreversibility, irregularity, multifractality, and short/long-tail distribution. Knowledge of the relationship between the form of the model and features of data seems to be the key to model time series. The paper presents a systematic analysis of the multiscale behavior of selected measures of irreversibility, irregularity, and non-stationarity vs degree of nonlinearity and persistence. As a time series generator, the modified nonlinear Langevin equation with built-in persistence is adopted. The modes of nonlinearity are determined by one parameter and do not change the half-Gaussian form of the marginal distribution function. The expected direct dependencies (sometimes non-trivial) were found and explained using the simplicity of the model. It has been shown that the change in nonlinearity, although subjected to a strong constraint (the same marginal distribution), causes significant changes in the tested markers of irregularity and non-stationarity. However, a synergy of non-linearity and persistence is needed to induce greater changes in irreversibility.

Automated summary

Stochastic models of time series can be nonlinear equations with a built-in memory mechanism. The generated time series can be characterized by certain features such as non-stationarity, irreversibility, irregularity, multifractality, and distribution type. This paper systematically analyzes the relationship between measures of irreversibility, irregularity, and non-stationarity and the degree of nonlinearity and persistence using a modified nonlinear Langevin equation. The results show that changes in nonlinearity affect irregularity and non-stationarity markers significantly, while a synergy of non-linearity and persistence is needed for greater changes in irreversibility.