Detecting dynamic spatial correlation patterns with generalized wavelet coherence and non-stationary surrogate data.

Area of Science:

• Complex Systems Analysis
• Time Series Data Science
• Signal Processing

Background:

• Real-world time series data are often characterized by noise, complexity, and evolving statistical properties.
• Standard methods struggle to detect transient spatial coherent patterns in such dynamic systems.
• Existing surrogate data methods may not preserve the amplitude and time-frequency characteristics of non-stationary data.

Purpose of the Study:

• To develop and evaluate a novel framework for detecting short-lived spatial coherent patterns in multivariate time series.
• To address the limitations of standard methods in analyzing complex, non-stationary real-world data.
• To provide insights into the time-resolved structure of spatially extended systems.

Main Methods:

• A new method combining wavelet analysis with non-stationary surrogate data generation.
• The proposed surrogate data are realizations of a non-stationary stochastic process.
• This approach preserves the amplitude and time-frequency distributions of the original multivariate time series.

Main Results:

• The framework successfully detects short-lived spatial coherent patterns in both synthetic and real-world time series.
• The non-stationary surrogate data accurately reflect the statistical properties of the original data.
• The method demonstrates superior performance compared to standard techniques for analyzing dynamic systems.

Conclusions:

• The presented method offers a robust approach for analyzing complex, non-stationary time series data.
• It provides valuable insights into the temporal dynamics and spatial structure of extended systems.
• This framework enhances the understanding of transient phenomena in multivariate data.