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

54 Pages Posted: 7 Sep 2021 Last revised: 3 Oct 2022

See all articles by Cole van Jaarsveldt

Cole van Jaarsveldt

Heriot-Watt University - Department of Actuarial Mathematics and Statistics

Gareth Peters

University of California Santa Barbara; University of California, Santa Barbara

Matthew Ames

ResilientML; The Institute of Statistical Mathematics

Mike J. Chantler

Heriot-Watt University - Department of Computer Science

Date Written: October 3, 2022

Abstract

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). In outlining a statistical perspective of the EMD method, it will be contrasted and combined (for the betterment of both methods) with other existing non-stationary basis decomposition methods. Some such techniques are functional Independent Component Analysis (ICA), Empirical Fourier Decomposition (EFD) (non-stationary extension of the Short-Time Fourier Transform (STFT)), Empirical Wavelet Transform (EWT) (non-stationary extension of Morlet Wavelet Transform (MWT)), and Singular Spectrum Decomposition (SSD) (non-stationary extension and refinement of Singular Spectrum Analysis (SSA)). A detailed review of this time series basis decomposition approach is presented that explores 3 core aspects for a statistical audience:

1. the basis functions (Intrinsic Mode Functions (IMFs)) representation and estimation methods including robustness and optimal spline representations including smoothing and knot placements;
2. the computational and numerical robustness of various aspects of the iterative algorithmic design for EMD basis extraction, including treating carefully boundary effects; and
3. the first attempt at a population-based characterisation of EMD that provides a novel stochastic embedding of the EMD method within a stochastic model framework.

Furthermore, the basis representations considered will be connected to 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.

Keywords: Time Series Analysis, Empirical Mode Decomposition, Fourier Analysis, Wavelet Analysis, Independent Component Analysis, X11, Non-Stationary, Graduation, Signal Decomposition

JEL Classification: C02, C14, C22, C32, C38

Suggested Citation

van Jaarsveldt, Cole and Peters, Gareth and Ames, Matthew and Ames, Matthew and Chantler, Michael John, Tutorial on Empirical Mode Decomposition: Basis Decomposition and Frequency Adaptive Graduation in Non-Stationary Time Series (October 3, 2022). Available at SSRN: https://ssrn.com/abstract=3913330 or http://dx.doi.org/10.2139/ssrn.3913330

Cole Van Jaarsveldt (Contact Author)

Heriot-Watt University - Department of Actuarial Mathematics and Statistics ( email )

Edinburgh, Scotland EH14 4AS
United Kingdom

Gareth Peters

University of California Santa Barbara ( email )

Santa Barbara, CA 93106
United States

University of California, Santa Barbara ( email )

Matthew Ames

ResilientML ( email )

Melbourne
Australia

The Institute of Statistical Mathematics ( email )

Tokyo
Japan

Michael John Chantler

Heriot-Watt University - Department of Computer Science

Edinburgh
United Kingdom

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