非线性系统
系列(地层学)
统计物理学
高斯分布
数学
时间序列
应用数学
朗之万方程
统计
物理
量子力学
生物
古生物学
作者
Monika Petelczyc,Zbigniew Czechowski
出处
期刊:Chaos
[American Institute of Physics]
日期:2023-05-01
卷期号:33 (5)
被引量:1
摘要
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.
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