Disentangling the stochastic behavior of complex time series

Area of Science:

• Complex Systems Dynamics
• Stochastic Processes
• Time Series Analysis

Background:

• Complex systems often display non-stationary dynamics with continuous or discontinuous time series.
• Distinguishing jump events from normal diffusion is crucial for understanding stochastic dynamics.
• Current methods face challenges in disentangling these effects.

Purpose of the Study:

• To introduce a non-parametric method for analyzing complex systems with both diffusive and jumpy dynamics.
• To develop a framework for separating deterministic drift from stochastic behaviors.
• To enable data-driven inference of model parameters from time series data.

Main Methods:

• Stochastic dynamical jump-diffusion modeling was employed.
• A non-parametric approach was used to estimate unknown functions and coefficients.
• The method was applied to empirical time series data.

Main Results:

• The method successfully separates deterministic drift from diffusive and jumpy stochastic behaviors.
• All unknown model components were derived directly from measured time series.
• The approach was demonstrated on brain dynamics data from epilepsy patients.

Conclusions:

• The developed method effectively disentangles jump-diffusion processes in complex systems.
• Inferred stochastic behaviors offer valuable information for diagnostic purposes.
• This technique enhances the understanding of brain dynamics and other complex systems.