A comparative analysis of iterative and variational decomposition strategies for wind speed forecasting: LMD and VMD

Abstract

This paper investigates the role of data preprocessing techniques in improving the forecasting performance of highly volatile time series. Although prior studies predominantly emphasize complex hybrid model architectures or extensive hyperparameter optimization, the isolated effect of the mathematical foundations of decomposition methods on prediction accuracy remains relatively underexplored. To address this issue, two fundamentally different decomposition techniques—Variational Mode Decomposition (VMD), which follows a variational optimization framework, and Local Mean Decomposition (LMD), which is based on an iterative scheme—are comparatively applied to nonlinear and highly fluctuating wind speed time series. Following decomposition, each extracted component is forecast individually and subsequently reconstructed using a Long Short-Term Memory (LSTM) network. In addition, an LSTM model trained directly on raw data is employed as a benchmark to assess the effectiveness of the proposed hybrid approaches. The experimental results demonstrate that incorporating a preprocessing stage substantially enhances forecasting accuracy. Both hybrid models outperform the baseline LSTM model in terms of prediction error metrics. Among them, the VMD-based approach yields the lowest error values and exhibits superior robustness and stability when compared with the LMD-based model. The statistical significance of the observed performance differences is further validated through the Diebold–Mariano test, confirming the dominance of the proposed VMD–LSTM framework at the 1% significance level (p < 0.01). Overall, the findings underline the critical importance of data preprocessing in forecasting tasks involving highly noisy and volatile time series and indicate that variational-based decomposition offers notable advantages in terms of stability and reproducibility over iterative methods.

Keywords

• Wind speed forecasting
• Data preprocessing
• Variational mode decomposition (VMD)
• Local mean decomposition (LMD)
• Long short-term memory (LSTM)

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