Refined Nonuniform Embedding For Coupling Detection In Multivariate Time Series

State-space reconstruction is essential to analyze the dynamics and internal interactions of complex systems. However, it is difficult to estimate high-dimensional conditional mutual information and select the optimal time delays in most existing nonuniform state-space reconstruction methods. Therefore, we propose a nonuniform embedding method framed in information theory for state-space reconstruction. We use a low-dimensional approximation of conditional mutual information criterion for time delay selection, which is effectively solved by the particle swarm optimization algorithm. The obtained embedded vector has relatively strong independence and low redundancy, which better characterizes multivariable complex systems and detects coupling within complex systems. In addition, the proposed nonuniform embedding method exhibits good performance in coupling detection of linear stochastic, nonlinear stochastic, chaotic systems. In the actual application, the importance of small airports that cause delay propagation has been demonstrated by constructing the delay propagation network.