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emd_local_median

EMD with Local Median Smoothing - Empirical Mode Decomposition using Epanechnikov kernel-weighted local median

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Created 2026-01-15
Last Updated 2026-02-19
Last Push 2026-01-18
Contributors 1
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Reproducibility

No specific reproducibility files found.

Status

  • Issues: Enabled
  • Wiki: Enabled
  • Pages: Enabled

README

EMD with Local Median Smoothing

Empirical Mode Decomposition using Epanechnikov kernel-weighted local median for robust signal decomposition.

Overview

This project presents a novel approach to EMD that uses kernel-weighted local median smoothing instead of traditional spline-based envelope methods. The local median approach provides:

  • Robustness: 50% breakdown point for outlier resistance
  • Smoothness: Epanechnikov kernel weighting for smooth estimates
  • Adaptivity: Data-driven bandwidth selection

Authors

  • Yezhou Sha
  • Volodia Spokoiny
  • Wolfgang Karl Hardle (HU Berlin)
  • David Siang-Li Jheng
  • Marc-Eduard Ionescu
  • Daniel Traian Pele

Affiliations: Humboldt-Universitat zu Berlin, MSCA Digital Finance, Bucharest University of Economic Studies

Key Formulas

Epanechnikov Kernel

K(u) = (3/4)(1 - u^2) for |u| <= 1

Local Median Estimator

m_hat(t) = weighted_median{ Y_s : s in [t-h, t+h], weighted by K((s-t)/h) }

EMD Iteration

r^(k+1)(t) = r^(k)(t) - m_hat^(k)(t)

Method Comparison

Property Local Median Median Average
Breakdown Point 50% 50% 0%
Kernel Weighted Yes No Yes
Outlier Robust Yes Yes No
Smoothness High Medium High

License

MIT License