Package AdvEMDpy: Algorithmic Variations of Empirical Mode Decomposition in Python

48 Pages Posted: 25 Oct 2021 Last revised: 19 Oct 2022

See all articles by Cole van Jaarsveldt

Cole van Jaarsveldt

Heriot-Watt University - Department of Actuarial Mathematics and Statistics

Matthew Ames

ResilientML; The Institute of Statistical Mathematics

Gareth Peters

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

Mike J. Chantler

Heriot-Watt University - Department of Computer Science

Date Written: September 29, 2022

Abstract

This work presents a Python EMD package named AdvEMDpy that is both more flexible, andwhich generalises, existing EMD packages in Python, R, and MATLAB. It is aimed specificallyfor use by the insurance and financial risk communities, for applications such as return modelling, claims modelling, and life insurance applications with a particular focus on mortality modelling. AdvEMDpy both expands upon the EMD options and methods available, and improves their statistical robustness and efficiency, providing a robust, usable, and reliable toolbox. Unlike many EMD packages, AdvEMDpy allows customisation by the user, to ensure that a broader class of linear, non-linear, and non-stationary time series analyses can be performed. The intrinsic mode functions (IMFs) extracted using EMD contain complex multi-frequency structures which warrant maximum algorithmic customisation for effective analysis. A major contribution of this package is the intensive treatment of the EMD edge effect which is the most ubiquitous problem in EMD and time series analysis. Various EMD techniques, of varying intricacy from numerous works, have been developed, refined, and, for the first time, compiled in AdvEMDpy. In addition to the EMD edge effect, numerous preprocessing, post-processing, detrended fluctuation analysis (localised trend estimation) techniques, stopping criteria, spline methods, discrete-time Hilbert transforms (DTHT), knot point optimisations, and other algorithmic variations have been incorporated and presented to the users of AdvEMDpy. This paper and the supplementary materials provide several real-world actuarial applications of this package for the user’s benefit.

Keywords: Empirical Mode Decomposition (EMD), Statistical EMD (SEMD), Enhanced EMD (EEMD), Ensemble EMD, Hilbert transform, time series analysis, filtering, graduation, Winsorization, downsampling, splines, knot optimisation, Python, R, MATLAB

JEL Classification: C02, C14, C22, C32, C61, C63, C65, C88

Suggested Citation

van Jaarsveldt, Cole and Ames, Matthew and Ames, Matthew and Peters, Gareth and Chantler, Michael John, Package AdvEMDpy: Algorithmic Variations of Empirical Mode Decomposition in Python (September 29, 2022). Available at SSRN: https://ssrn.com/abstract=3947132 or http://dx.doi.org/10.2139/ssrn.3947132

Cole Van Jaarsveldt (Contact Author)

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

Edinburgh, Scotland EH14 4AS
United Kingdom

Matthew Ames

ResilientML ( email )

Melbourne
Australia

The Institute of Statistical Mathematics ( email )

Tokyo
Japan

Gareth Peters

University of California Santa Barbara ( email )

Santa Barbara, CA 93106
United States

University of California, Santa Barbara ( email )

Michael John Chantler

Heriot-Watt University - Department of Computer Science

Edinburgh
United Kingdom

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