{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T00:38:50Z","timestamp":1773103130518,"version":"3.50.1"},"reference-count":81,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T00:00:00Z","timestamp":1773014400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University","award":["IMSIU-DDRSP2602"],"award-info":[{"award-number":["IMSIU-DDRSP2602"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Modeling nonstationary time series in financial and energy markets remains challenging due to nonlinear dynamics, volatility clustering, and frequent regime shifts that distort the underlying probabilistic structure of the data. This study introduces a novel probabilistic\u2013statistical decomposition framework, termed Robust Adaptive Decomposition (RAD), designed to preserve probabilistic symmetry between deterministic and stochastic components. In this context, symmetry refers to maintaining statistical balance\u2014particularly in the means, variances, and distributional structures\u2014between the extracted modes and the residual series, thereby preventing artificial bias or variance distortion during decomposition. The RAD framework adaptively determines the optimal number of modes needed to effectively separate short-term fluctuations from long-term structural movements. Unlike conventional techniques, such as Empirical Mode Decomposition (EMD), Ensemble EMD (EEMD), and CEEMDAN, the proposed method incorporates a robustness mechanism that mitigates mode mixing and reduces distortions induced by extreme shocks and regime transitions. The empirical evaluation is conducted on six oil-related energy commodities\u2014Brent crude oil, kerosene, propane, sulfur diesel, heating oil, and gasoline\u2014whose price dynamics exhibit pronounced nonlinearity and structural volatility. When integrated with ARIMA forecasting models, the RAD-based framework consistently outperforms benchmark decomposition approaches. Across all datasets, RAD\u2013ARIMA achieves reductions of approximately 65\u201390% in MAE, 60\u201385% in RMSE, and up to 95% in MAPE relative to CEEMDAN-based models. These results demonstrate that RAD provides a mathematically rigorous and computationally efficient preprocessing mechanism that preserves statistical equilibrium while effectively disentangling deterministic structures from stochastic noise. Beyond oil markets, the framework offers broad applicability in econometric modeling, financial forecasting, and risk management, contributing to probability- and statistics-driven symmetry analysis in complex dynamic systems.<\/jats:p>","DOI":"10.3390\/sym18030465","type":"journal-article","created":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T13:27:18Z","timestamp":1773062838000},"page":"465","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Decomposition-Driven Hybrid Approach to Forecasting Oil Market Dynamics"],"prefix":"10.3390","volume":"18","author":[{"given":"Laiba Sultan","family":"Dar","sequence":"first","affiliation":[{"name":"Department of Statistics, Abdul Wali Khan University, Mardan 23200, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5758-1035","authenticated-orcid":false,"given":"Mahmoud M.","family":"Abdelwahab","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1895-5350","authenticated-orcid":false,"given":"Muhammad","family":"Aamir","sequence":"additional","affiliation":[{"name":"Department of Statistics, Abdul Wali Khan University, Mardan 23200, Pakistan"}]},{"given":"Moeeba","family":"Rind","sequence":"additional","affiliation":[{"name":"Department of Education, Abasyn University, Peshawar 25000, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1248-9910","authenticated-orcid":false,"given":"Paulo Canas","family":"Rodrigues","sequence":"additional","affiliation":[{"name":"Department of Statistics, Federal University of Bahia, Salvador 40170-110, Brazil"},{"name":"Department of Business Management, University of Pretoria, Pretoria 0002, South Africa"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9043-9644","authenticated-orcid":false,"given":"Mohamed A.","family":"Abdelkawy","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Nasir, J., Iftikhar, H., Aamir, M., Iftikhar, H., Rodrigues, P.C., and Rehman, M.Z. 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