[Paper Review] Detecting dynamic spatial correlation patterns with generalized wavelet coherence and non-stationary surrogate data

Mario Chávez, Bernard Cazelles|arXiv (Cornell University)|Jan 15, 2018

Complex Systems and Time Series AnalysisEconomics, Econometrics and Finance40 references57 citations

TL;DR

The paper develops a wavelet-based framework to detect short-lived, time-varying spatial coherence among multivariate time series by using non-stationary surrogate data, and validates it on synthetic and real data (EEG and measles).

ABSTRACT

Time series measured from real-world systems are generally noisy, complex and display statistical properties that evolve continuously over time. Here, we present a method that combines wavelet analysis and non-stationary surrogates to detect short-lived spatial coherent patterns from multivari- ate time-series. In contrast with standard methods, the surrogate data used here are realisations of a non-stationary stochastic process, preserving both the amplitude and time-frequency distributions of original data. We evaluate this framework on synthetic and real-world time series, and we show that it can provide useful insights into the time-resolved structure of spatially extended systems.

Motivation & Objective

• Motivate the need to detect transient spatial synchrony in noisy, non-stationary systems.
• Generalize wavelet coherence to multivariate signals to capture time-frequency complex relationships.
• Introduce non-stationary surrogate data that preserve amplitude and time-frequency distributions.
• Assess statistical significance of transient coherence via Monte Carlo surrogates and FDR correction.
• Demonstrate advantages over stationary surrogates on synthetic and real-world datasets.

Proposed method

• Use continuous Morlet wavelets to compute time-frequency cross-spectra between signals.
• Define a multivariate coherence matrix at each time-frequency point and derive TVSC: Ψ(t,f) = (λ_max^Σ(t,f) − 1)/(M−1).
• Extend surrogate testing to the time-frequency domain to preserve both amplitude and TF energy distributions.
• Generate non-stationary surrogates by randomizing phase in the wavelet domain while preserving original TF distributions, with iterative amplitude adjustment.
• Assess significance via z-tests against surrogate distributions and control for multiple testing with FDR (q ≤ 0.05).
• Validate on synthetic AR and Rössler networks and on real EEG and measles time series.

Experimental results

Research questions

• RQ1 Can generalized wavelet coherence capture transient, time-varying spatial correlations in multivariate non-stationary data?
• RQ2 Do non-stationary surrogates preserve time-frequency structure better than classical surrogates, improving significance testing?
• RQ3 How does TVSC Ψ(t,f) behave in synthetic nonlinear systems and real-world datasets (EEG, measles) during changing synchronization patterns?
• RQ4 Is the proposed surrogate-based significance testing robust to edge effects and multiple comparisons across the time-frequency plane?

Key findings

• Ψ(t,f) provides a bounded measure (0 to 1) of time-varying spatial coherence across M signals.
• Non-stationary surrogates better replicate TF structure than stationary or DWT-based surrogates, reducing false coherent patches.
• In EEG, non-stationary surrogates sharpen TF localization of coherence and reveal desynchronization before seizure propagation and synchronized spreading during seizures.
• In measles data, Ψ(t,f) detects high spatial coherence in the pre-vaccine biennial component and decorrelation post-vaccination.
• Compared to iAAFT and iAAWT surrogates, the non-stationary surrogate approach yields fewer spurious coherence regions and more accurate synchronization detection.
• The framework outperforms stationary surrogate tests and standard DWT-based methods in both synthetic and real datasets.