How to extract the oscillating components of a signal? A wavelet-based approach compared to the Empirical Mode Decomposition

Researchers are often confronted with time series that display pseudo-periodic tendencies with time-varying amplitudes and frequencies. In that framework, a classic Fourier analysis of the data may be of limited interest, especially if the objective is to derive components from the signal that capture the non-stationary behaviour of the oscillating factors. In this talk, we present two powerful tools designed to extract amplitude modulated-frequency modulated (AM-FM) components from a given signal. The first one is the renowned Empirical Mode Decomposition (EMD); we explain the technique, its main benefits, limitations and major practical uses. Then, we introduce the continuous wavelet transform and the equations that justify its relevance in the present context. We propose an algorithm based on the wavelet-induced time-frequency representation of a signal to extract its main components. The performances of this method are compared with the EMD on various AM-FM signals exhibiting different particularities. After briefly broaching the problem of edge effects, we investigate whether the wavelet-based procedure can be used in the domain of time series forecasting. For that purpose, we study the El Nino Southern Oscillation index and develop a model aimed at predicting the long-term trends of the signal. Its predictive skills are tested in several ways and exposed in the final part of the talk.