Adaptive Variational Mode Decomposition via RIME Optimization and Fuzzy Entropy for PatchTST-Based Financial Time-Series Forecasting
The inherent non-linear, non-stationary, multi-scale nature of financial time-series data makes the task of financial forecasting exceptionally difficult. While deep learning models incorporating decomposition techniques have achieved significant progress in forecasting, their performance heavily re...
Guardado en:
| Autores principales: | , , , , , |
|---|---|
| Formato: | Artículo |
| Lenguaje: | inglés |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | Enlace permanente (DOI o Handle) |
| Etiquetas: |
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1881700531171229696 |
|---|---|
| author | Jawaria Nasir Moiz Qureshi Yasir Hussain Muhammad Junaid Javier Linkolk López‐Gonzales Ronny Ivan Gonzales Medina |
| author_browse | Javier Linkolk López‐Gonzales Jawaria Nasir Moiz Qureshi Muhammad Junaid Ronny Ivan Gonzales Medina Yasir Hussain |
| author_facet | Jawaria Nasir Moiz Qureshi Yasir Hussain Muhammad Junaid Javier Linkolk López‐Gonzales Ronny Ivan Gonzales Medina |
| author_sort | Jawaria Nasir |
| collection | Producción científica |
| description | The inherent non-linear, non-stationary, multi-scale nature of financial time-series data makes the task of financial forecasting exceptionally difficult. While deep learning models incorporating decomposition techniques have achieved significant progress in forecasting, their performance heavily relies on the signal’s quality during decomposition and the setting of parameters. To this end, this study presents a forecasting framework for the S&P 500 index using RFEO–VMD–PatchTST (RIME and Fuzzy Entropy Optimized Variational Mode Decomposition with PatchTST). We utilized the RIME optimization algorithm to autonomously obtain VMD’s optimal number of modes K and penalty term. To identify which is the best-performing model among the evaluated models under the reported test protocol, i.e., Sample Entropy (SE), Fuzzy Entropy (FE), and Permutation Entropy (PE), were discussed and used as objectives for optimization. In particular, the experimental analysis showed that Fuzzy Entropy achieves better decomposition quality with K = 2, producing two adaptive IMFs and yields the optimal decomposition that represents the primary driving forces of market trends. Subsequently, we independently model each IMF using the Patch Time Series Transformer (PatchTST) and then combine the IMF forecasts to obtain the final prediction. Experiments with various evaluation criteria were conducted on S&P 500 index data, and the results show that our framework consistently outperforms conventional methods, including statistical, machine learning, deep learning, and decomposition-based approaches. Additionally, to verify that our framework is robust, stable, and statistically significant, we provide ablation studies, multi-horizon forecasting, rolling-window analysis, random-seed experiments, and Diebold–Mariano tests. |
| format | Article |
| id | openalex:W7222976568 |
| institution | UPeU |
| language | English |
| publishDate | 2026 |
| publishDateRange | 2026 |
| publishDateSort | 2026 |
| record_format | dspace |
| spelling | openalex:W7222976568Adaptive Variational Mode Decomposition via RIME Optimization and Fuzzy Entropy for PatchTST-Based Financial Time-Series ForecastingJawaria NasirMoiz QureshiYasir HussainMuhammad JunaidJavier Linkolk López‐GonzalesRonny Ivan Gonzales Medinavariational mode decompositionfuzzy entropysample entropypermutation entropyPatchTSTfinancial time series forecastingS&P 500multi-scale decompositionensemble forecastingmulti-horizon forecastingDiebold-Mariano testStock Market Forecasting MethodsTime Series Analysis and ForecastingForecasting Techniques and ApplicationsThe inherent non-linear, non-stationary, multi-scale nature of financial time-series data makes the task of financial forecasting exceptionally difficult. While deep learning models incorporating decomposition techniques have achieved significant progress in forecasting, their performance heavily relies on the signal’s quality during decomposition and the setting of parameters. To this end, this study presents a forecasting framework for the S&P 500 index using RFEO–VMD–PatchTST (RIME and Fuzzy Entropy Optimized Variational Mode Decomposition with PatchTST). We utilized the RIME optimization algorithm to autonomously obtain VMD’s optimal number of modes K and penalty term. To identify which is the best-performing model among the evaluated models under the reported test protocol, i.e., Sample Entropy (SE), Fuzzy Entropy (FE), and Permutation Entropy (PE), were discussed and used as objectives for optimization. In particular, the experimental analysis showed that Fuzzy Entropy achieves better decomposition quality with K = 2, producing two adaptive IMFs and yields the optimal decomposition that represents the primary driving forces of market trends. Subsequently, we independently model each IMF using the Patch Time Series Transformer (PatchTST) and then combine the IMF forecasts to obtain the final prediction. Experiments with various evaluation criteria were conducted on S&P 500 index data, and the results show that our framework consistently outperforms conventional methods, including statistical, machine learning, deep learning, and decomposition-based approaches. Additionally, to verify that our framework is robust, stable, and statistically significant, we provide ablation studies, multi-horizon forecasting, rolling-window analysis, random-seed experiments, and Diebold–Mariano tests.Articlehttps://doi.org/10.3390/stats9050116W7222976568enStats2571-905X2026-10-19 |
| spellingShingle | variational mode decomposition fuzzy entropy sample entropy permutation entropy PatchTST financial time series forecasting S&P 500 multi-scale decomposition ensemble forecasting multi-horizon forecasting Diebold-Mariano test Stock Market Forecasting Methods Time Series Analysis and Forecasting Forecasting Techniques and Applications Jawaria Nasir Moiz Qureshi Yasir Hussain Muhammad Junaid Javier Linkolk López‐Gonzales Ronny Ivan Gonzales Medina Adaptive Variational Mode Decomposition via RIME Optimization and Fuzzy Entropy for PatchTST-Based Financial Time-Series Forecasting |
| title | Adaptive Variational Mode Decomposition via RIME Optimization and Fuzzy Entropy for PatchTST-Based Financial Time-Series Forecasting |
| title_full | Adaptive Variational Mode Decomposition via RIME Optimization and Fuzzy Entropy for PatchTST-Based Financial Time-Series Forecasting |
| title_fullStr | Adaptive Variational Mode Decomposition via RIME Optimization and Fuzzy Entropy for PatchTST-Based Financial Time-Series Forecasting |
| title_full_unstemmed | Adaptive Variational Mode Decomposition via RIME Optimization and Fuzzy Entropy for PatchTST-Based Financial Time-Series Forecasting |
| title_short | Adaptive Variational Mode Decomposition via RIME Optimization and Fuzzy Entropy for PatchTST-Based Financial Time-Series Forecasting |
| title_sort | adaptive variational mode decomposition via rime optimization and fuzzy entropy for patchtst based financial time series forecasting |
| topic | variational mode decomposition fuzzy entropy sample entropy permutation entropy PatchTST financial time series forecasting S&P 500 multi-scale decomposition ensemble forecasting multi-horizon forecasting Diebold-Mariano test Stock Market Forecasting Methods Time Series Analysis and Forecasting Forecasting Techniques and Applications |
| topic_facet | variational mode decomposition fuzzy entropy sample entropy permutation entropy PatchTST financial time series forecasting S&P 500 multi-scale decomposition ensemble forecasting multi-horizon forecasting Diebold-Mariano test Stock Market Forecasting Methods Time Series Analysis and Forecasting Forecasting Techniques and Applications |
| url | https://doi.org/10.3390/stats9050116 |
| work_keys_str_mv | AT jawarianasir adaptivevariationalmodedecompositionviarimeoptimizationandfuzzyentropyforpatchtstbasedfinancialtimeseriesforecasting AT moizqureshi adaptivevariationalmodedecompositionviarimeoptimizationandfuzzyentropyforpatchtstbasedfinancialtimeseriesforecasting AT yasirhussain adaptivevariationalmodedecompositionviarimeoptimizationandfuzzyentropyforpatchtstbasedfinancialtimeseriesforecasting AT muhammadjunaid adaptivevariationalmodedecompositionviarimeoptimizationandfuzzyentropyforpatchtstbasedfinancialtimeseriesforecasting AT javierlinkolklopezgonzales adaptivevariationalmodedecompositionviarimeoptimizationandfuzzyentropyforpatchtstbasedfinancialtimeseriesforecasting AT ronnyivangonzalesmedina adaptivevariationalmodedecompositionviarimeoptimizationandfuzzyentropyforpatchtstbasedfinancialtimeseriesforecasting |