{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T06:00:30Z","timestamp":1787032830974,"version":"build-2736575974"},"reference-count":37,"publisher":"PeerJ","license":[{"start":{"date-parts":[[2024,10,8]],"date-time":"2024-10-08T00:00:00Z","timestamp":1728345600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Product prices frequently manifest nonlinear and nonstationary time-series attributes, indicating potential variations in their behavioral patterns over time. Conventional linear models may fall short in adequately capturing these intricate properties. In addressing this, the present study leverages the adaptive and non-recursive attributes of the Variational Mode Decomposition (VMD) methodology. It employs VMD to dissect the intricate time series into multiple Intrinsic Mode Functions (IMF). Subsequently, a method rooted in the minimum fuzzy entropy criterion is introduced for determining the optimal modal number (K) in the VMD decomposition process. This method effectively mitigates issues related to modal confusion and endpoint effects, thereby enhancing the decomposition efficacy of VMD. In the subsequent phase, deep neural networks (DNN) are harnessed to forecast the identified modes, with the cumulative modal predictions yielding the ultimate e-commerce product price prognostications. The predictive efficacy of the proposed Variational Mode Decomposition-deep neural network (VMD-DNN) decomposition model is assessed on three public datasets, wherein the mean absolute percentage error (MAPE) on the E-commerce Price Prediction Dataset and Online Retail Dataset is notably low at 0.6578 and 0.5414, respectively. This corresponds to a remarkable error reduction rate of 66.5% and 70.4%. Moreover, the VMD-DNN decomposition model excels in predicting e-commerce product prices through DNN, thereby amplifying the VMD decomposition capability by 4%. The VMD-DNN model attains superior results in terms of directional symmetry, boasting the highest Directional Symmetry (DS) score of 86.25. Notably, the forecasted trends across diverse price ranges closely mirror the actual trends.<\/jats:p>","DOI":"10.7717\/peerj-cs.2353","type":"journal-article","created":{"date-parts":[[2024,10,8]],"date-time":"2024-10-08T03:57:57Z","timestamp":1728359877000},"page":"e2353","source":"Crossref","is-referenced-by-count":3,"title":["Predicting e-commerce product prices through the integration of variational mode decomposition and deep neural networks"],"prefix":"10.7717","volume":"10","author":[{"given":"Haojie","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Business Administration, Shanxi Polytechnic College, Taiyuan, Shanxi, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"4443","published-online":{"date-parts":[[2024,10,8]]},"reference":[{"key":"10.7717\/peerj-cs.2353\/ref-1","doi-asserted-by":"publisher","first-page":"104862","DOI":"10.1016\/j.eneco.2020.104862","article-title":"Global factors, uncertainty, weather conditions and energy 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