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Updated: May 26, 2026

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WHiAR-Net: an interpretable multi-scale forecasting framework via Wavelet-Hilbert feature engineering.

Kai-Cheng Wang1

  • 1Department of Mathematics and Applied Mathematics, School of Information Engineering, Sanming University, Sanming City, 365004, Fujian, China. gtotony98@gmail.com.

Scientific Reports
|May 24, 2026
PubMed
Summary
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Forecasting complex time series is difficult. Our new WHiAR-Net framework uses wavelet theory and Hilbert spectral analysis for accurate, interpretable predictions, outperforming deep learning models.

Area of Science:

  • Time Series Analysis
  • Signal Processing
  • Machine Learning

Background:

  • Accurate forecasting of non-stationary time series is crucial but challenging due to complex volatility.
  • Conventional black-box models often lack interpretability and transparency.

Purpose of the Study:

  • To introduce WHiAR-Net, an interpretable framework for accurate non-stationary time series forecasting.
  • To provide a principled alternative to black-box models by integrating wavelet theory and Hilbert spectral analysis.

Main Methods:

  • Developed WHiAR-Net, a novel framework combining wavelet theory and Hilbert spectral analysis.
  • Structurally embedded operator error bounds for enhanced transparency and interpretability.
  • Separated long-term trends from transient fluctuations within the time series.
Keywords:
Hilbert transformInterpretable machine learningTime series forecastingWavelet

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Main Results:

  • WHiAR-Net demonstrated highly competitive accuracy on electricity and environmental datasets.
  • The proposed method outperformed modern deep learning baselines in forecasting accuracy.
  • The framework offers superior interpretability compared to conventional models.

Conclusions:

  • WHiAR-Net provides an accurate and interpretable solution for non-stationary time series forecasting.
  • The framework has promising applications in smart energy grids and climate monitoring.
  • This approach offers a principled alternative to complex black-box forecasting models.