Maryam Maatallah, Mourad Fariss, Hakima Asaidi, Mohamed Bellouki
This study proposes a framework combining Variational Mode Decomposition (VMD) with a relevance-driven selection process to reduce noise and redundancy in financial time-series forecasting. The original time series is decomposed by VMD into intrinsic mode functions (IMFs), which are then evaluated using three relevance metrics: relative energy contribution, mutual information, and Spearman's rank correlation coefficient. These metrics identify the IMFs most strongly associated with future price movements. As opposed to conventional VMD-based approaches that treat all IMFs equally, the proposed relevance-driven selection process adapts IMF selection to the statistical properties of the analyzed market, thereby improving model generalization across different volatility conditions and forecasting horizons. This study makes three main contributions: (i) developing a relevance-driven IMF selection strategy to overcome limitations of traditional VMD methods, (ii) designing a hybrid framework that integrates multiscale decomposition with nonlinear information filtering, and (iii) conducting a comprehensive empirical evaluation of the proposed models. Experiments on hourly Bitcoin (BTC)/USD data from 2018 to 2025 show that the VMD-RDIC-deep learning models achieves strong forecasting performance. The results show that the proposed relevance-driven decomposition framework improves prediction accuracy and robustness compared with traditional statistical models, including Autoregressive Integrated Moving Average (ARIMA), as well as machine learning and deep learning approaches, highlighting its suitability for complex and volatile financial markets. Received: 18 January 2026 | Revised: 13 April 2026 | Accepted: 23 July 2026 Conflicts of Interest The authors declare that they have no conflicts of interest to this work. Data Availability Statement The data that support the findings of this study are openly available at https://www.kaggle.com/datasets/novandraanugrah/bitcoin-historical-datasets-2018-2024. Author Contribution Statement Maryam Maatallah: Conceptualization, Methodology, Software, Data curation, Writing β original draft, Visualization. Mourad Fariss: Software, Formal analysis, Writing β original draft. Hakima Asaidi: Validation, Investigation, Writing β review & editing. Mohamed Bellouki: Resources, Writing β review & editing, Supervision, Project administration.