Spectral and wavelet methods for the analysis of nonlinear and nonstationary time series

Abstract Higher order spectral methods are widely used to analyse stationary nonGaussian signals. Using the evolutionary spectral approach, we develop methods for evaluating evolutionary bispectrum (time dependent bispectrum) and illustrate the approach with examples. We also define wavelet transforms for discrete parameter time series, and show that higher order moments of these transforms are necessary to study nonlinear signals. The methods are illustrated with examples.

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