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Surrogates are investigated as procedures of synthesis for multi-variate time series with prescribed properties. First it is shown how to prescribe a multivariate covariance function jointly with the (possibly non-Gaussian) marginal distributions. Second, using histogram matching by approximate optimal transport with the Sliced Wasserstein Distance, the surrogate synthesis is extended to prescribe...
An operational framework is developed for testing stationarity relatively to an observation scale. The proposed method makes use of a family of stationary surrogates for defining the null hypothesis of stationarity. As a further contribution to the field, we demonstrate the strict-sense stationarity of surrogate signals and we exploit this property to derive the asymptotic distributions of their spectrogram...
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