Tutorial on Empirical Mode Decomposition: Basis Decomposition and Frequency Adaptive Graduation in Non-Stationary Time Series

This tutorial explores the class of non-parametric time series basis decomposition methods particularly suited for non-stationary time series known as Empirical Mode Decomposition (EMD). A detailed review of the state of the art statistical approaches that combine finite basis signal decomposition methods with smoothing graduation methods to characterise a non-stationary time series, where the representation is locally adapted to the frequency content of the signal, is addressed. Furthermore, the proposed EMD method also accommodates a variety of statistical properties including robustness to outliers and noise of various forms, regular or irregular sampling intervals such as with event-driven observations, and a variety of forms of non-stationarity. In outlining a statistical perspective of the EMD method, it will be contrasted with other existing basis decomposition methods such as functional Independent Component Analysis, Short-Time Fourier Transform, and Morlet Wavelet Analysis methods. Furthermore, the basis representations considered will be connected to versions of local frequency graduation smoothing methods, demonstrating that these can be adapted to a local frequency adaptive framework within the EMD context. This will provide new practical insights into the interface between time series basis decomposition and graduation smoothed representations.