![]() Recently, parametric models have been also applied to test wider classes of null hypothesis, including non-stationary behaviour 17, 18. Indeed, time-varying spectral properties (or any relevant description of these characteristics) are generally indicators of non-stationarity 19, or non-autonomous dynamics 20. Such properties are incompatible with the main assumptions of standard surrogate data based on Fourier transform 14, 15, 16, 17, 18. However, time series measurements from real systems generally display irregular fluctuations, long-term trends, or a time-varying spectra. Surrogate data techniques have been proposed as non-parametric resampling methods for testing general hypotheses on data without making assumptions on the underlying generating process 11, 12, 13. A rigorous theoretical framework cannot therefore be derived, and Monte Carlo simulations have to be performed to estimate the significance level 7, 8, 9, 10. Unfortunately, the statistical assumptions of these tests are not always compatible with the structure of the data considered, and significance levels often depend on the structure of the wavelets applied 7, 8, 9, 10. In recent years, different significance tests for the wavelet cross-spectrum or wavelet coherence have been developed to detect oscillatory patterns with covarying dynamics 4, 5, 6, 7, 8, 9, 10. neural oscillations, business cycles, climate variations or epidemics dynamics 2, 3, 4, 5. Among them, measures of synchrony or coherence based on wavelet transforms have been widely used to detect interactions between oscillatory components in different real systems, i. Synchrony estimators based on nonparametric methods have the advantage of not requiring any assumption on the time-scale structure of the observed signals. Statistical significance of transient coherent patterns cannot be assessed by classical spectral measures and tests, which require signals to be stationary 4, 5, 6. At various points throughout this paper, the terms synchrony and coherence are interchangeably used to describe the degree to which different process evolve in a similar way. Coherence is generally defined as the correlation between concurrent time series of a variable measured from several processes, whereas synchrony is referred to as the degree to which their fluctuations behave similarly over time 1. The statistical detection of spatial synchrony in networks of coupled dynamical systems is therefore of great interest in disciplines such as geophysics, physiology and ecology 2, 3, 4, 5. The interactions between coupled oscillators in real systems continuously create and destroy synchronised states, which can be observed as noisy and transient coherent patterns. Synchronization is a fundamental phenomenon described in many biological and physical contexts for which there are two or more interacting oscillatory systems 1. ![]()
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