{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T05:57:43Z","timestamp":1781243863906,"version":"3.54.1"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T00:00:00Z","timestamp":1781222400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T00:00:00Z","timestamp":1781222400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["72071001"],"award-info":[{"award-number":["72071001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["72371001"],"award-info":[{"award-number":["72371001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Excellent Young Talent Project of Colleges and Universities in Anhui Province","award":["gxyqZD2022001"],"award-info":[{"award-number":["gxyqZD2022001"]}]},{"name":"Outstanding Youth Foundation of Colleges and Universities in Anhui Province","award":["2023AH020009"],"award-info":[{"award-number":["2023AH020009"]}]},{"DOI":"10.13039\/501100003995","name":"Anhui Provincial Natural Science Foundation","doi-asserted-by":"crossref","award":["2408085Y035"],"award-info":[{"award-number":["2408085Y035"]}],"id":[{"id":"10.13039\/501100003995","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Humanity and Social Science Research Project of Anhui Educational Committee","award":["2024AH052196"],"award-info":[{"award-number":["2024AH052196"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cogn Comput"],"published-print":{"date-parts":[[2026,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Crude oil, as an important energy source, plays a pivotal role in global economic development. However, due to the dynamic nature and characteristics of crude oil data, which are affected by the uncertainty of market volatility and complex price change mechanisms, the existing crude oil price forecasting methods are ineffective. Therefore, we propose a novel crude oil price combinatorial link prediction method based on the MF-VMD-CDVGNets-SLRNN model, which converts crude oil price data into a periodic directed visible graph network. Compared with traditional forecasting methods, it can comprehensively analyze multi-period historical data and current data, derive the intrinsic characteristics of the data, and solve the problem of information loss in historical data. First, the original data are denoised and then decomposed and reconstructed into a sequence of components with different frequencies. The periodicity of each component is determined by applying the Fast Fourier Transform (FFT). Next, a Cyclic Directed Visibility Graph Network (CDVGNet) is employed to convert these components into a network that reflects the periodic structure of the time series. A random walk algorithm is then applied to measure the similarity between nodes across different temporal periods. In addition to extracting multi-period historical and current data features as prediction inputs, the method optimizes the convergence of the algorithm by controlling the network size. Finally, the combined prediction utilizes multiple artificial intelligence models, taking into account the nonlinear relationship between nodes. To validate the effectiveness of the proposed method, we conducted a West Texas Intermediate (WTI) crude oil price prediction experiment. The results show that the proposed method has higher prediction accuracy compared to other baseline methods.<\/jats:p>","DOI":"10.1007\/s12559-026-10613-7","type":"journal-article","created":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T02:24:49Z","timestamp":1781231089000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Novel Crude Oil Price Combination Link Forecasting Method based on the MF-VMD-CDVGNets-SLRNN Model"],"prefix":"10.1007","volume":"18","author":[{"given":"Xiaoman","family":"Zhao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinpei","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rui","family":"Luo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huayou","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhifu","family":"Tao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,12]]},"reference":[{"key":"10613_CR1","doi-asserted-by":"publisher","first-page":"106531","DOI":"10.1016\/j.eneco.2023.106531","volume":"119","author":"H Qu","year":"2023","unstructured":"Qu H, Li G. Multi-perspective investor attention and oil futures volatility forecasting. Energy Econ. 2023;119:106531.","journal-title":"Energy Econ"},{"key":"10613_CR2","doi-asserted-by":"publisher","first-page":"5219","DOI":"10.1080\/00207543.2016.1162340","volume":"54","author":"V Azevedo","year":"2016","unstructured":"Azevedo V, Campos L. Combination of forecasts for the price of crude oil on the spot market. Int J Prod Res. 2016;54:5219\u201335.","journal-title":"Int J Prod Res"},{"key":"10613_CR3","doi-asserted-by":"publisher","first-page":"102244","DOI":"10.1016\/j.resourpol.2021.102244","volume":"74","author":"K Drachal","year":"2021","unstructured":"Drachal K. Forecasting crude oil real prices with averaging time-varying VAR models. Resour Policy. 2021;74:102244.","journal-title":"Resour Policy"},{"issue":"15","key":"10613_CR4","first-page":"578","volume":"155","author":"A De","year":"2018","unstructured":"De A, De M, Da N, Maia S. Forecasting crude oil price: Does exist an optimal econometric model? Energy. 2018;155(15):578\u201391.","journal-title":"Energy"},{"key":"10613_CR5","doi-asserted-by":"publisher","first-page":"106405","DOI":"10.1016\/j.eneco.2022.106405","volume":"116","author":"Y Wang","year":"2022","unstructured":"Wang Y, Hao X. Forecasting the real prices of crude oil: A robust weighted least squares approach. Energy Economics. 2022;116:106405.","journal-title":"Energy Economics"},{"key":"10613_CR6","doi-asserted-by":"publisher","first-page":"104648","DOI":"10.1016\/j.eneco.2019.104648","volume":"86","author":"S Zhen","year":"2020","unstructured":"Zhen S, Zheng Q, Yang S, Gao F, Cheng M, Zhang Q, et al. Modeling and forecasting the electricity clearing price: A novel BELM based pattern classification framework and a comparative analytic study on multi-layer BELM and LSTM. Energy Economics. 2020;86:104648.","journal-title":"Energy Economics"},{"key":"10613_CR7","doi-asserted-by":"publisher","first-page":"107760","DOI":"10.1016\/j.asoc.2021.107760","volume":"112","author":"Y Chen","year":"2021","unstructured":"Chen Y, Huang W. Constructing a stock-price forecast CNN model with gold and crude oil indicators. Appl Soft Comput. 2021;112:107760.","journal-title":"Appl Soft Comput"},{"key":"10613_CR8","doi-asserted-by":"publisher","first-page":"105129","DOI":"10.1016\/j.eneco.2021.105129","volume":"95","author":"Q Nguyen","year":"2021","unstructured":"Nguyen Q, Diaz-Rainey I, Kuruppuarachchi D. Predicting corporate carbon footprints for climate finance risk analyses: a machine learning approach. Energy Economics. 2021;95:105129.","journal-title":"Energy Economics"},{"issue":"5","key":"10613_CR9","doi-asserted-by":"publisher","first-page":"1748","DOI":"10.1007\/s12559-023-10136-5","volume":"15","author":"J Lai","year":"2023","unstructured":"Lai J, Chen Z, Zhu J, et al. Deep learning based traffic prediction method for digital twin network. Cogn Comput. 2023;15(5):1748\u201366.","journal-title":"Cogn Comput"},{"key":"10613_CR10","doi-asserted-by":"publisher","first-page":"656","DOI":"10.1016\/j.eneco.2017.12.035","volume":"78","author":"F Cheng","year":"2019","unstructured":"Cheng F, Li T, Wei Y, Fan T. The VEC-NAR model for short-term forecasting of oil prices. Energy Economics. 2019;78:656\u201367.","journal-title":"Energy Economics"},{"key":"10613_CR11","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1016\/j.eneco.2017.05.023","volume":"66","author":"Y Zhao","year":"2017","unstructured":"Zhao Y, Li J, Yu LAA. A deep learning ensemble approach for crude oil price forecasting. Energy Econ. 2017;66:9\u201316.","journal-title":"Energy Econ"},{"key":"10613_CR12","doi-asserted-by":"publisher","first-page":"113686","DOI":"10.1016\/j.eswa.2020.113686","volume":"161","author":"B Wang","year":"2020","unstructured":"Wang B, Wang J. Deep multi-hybrid forecasting system with random EWT extraction and variational learning rate algorithm for crude oil futures. Expert Syst Appl. 2020;161:113686.","journal-title":"Expert Syst Appl"},{"issue":"3","key":"10613_CR13","first-page":"547","volume":"11","author":"G Kim","year":"2023","unstructured":"Kim G, Jang B. Petroleum price prediction with CNN-LSTM and CNN-GRU using skip-connection. Mathematics (Basel). 2023;11(3):547.","journal-title":"Mathematics (Basel)"},{"key":"10613_CR14","doi-asserted-by":"publisher","first-page":"125955","DOI":"10.1016\/j.energy.2022.125955","volume":"263","author":"C Rao","year":"2023","unstructured":"Rao C, Zhang Y, Wen J, Xiao X, Goh M. Energy demand forecasting in China: A support vector regression-compositional data second exponential smoothing model. Energy. 2023;263:125955.","journal-title":"Energy"},{"issue":"1","key":"10613_CR15","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/s12559-023-10203-x","volume":"16","author":"J Wang","year":"2024","unstructured":"Wang J, Liu J. Two-stage deep ensemble paradigm based on optimal multi-scale decomposition and multi-factor analysis for stock price prediction. Cogn Comput. 2024;16(1):243\u201364.","journal-title":"Cogn Comput"},{"issue":"08","key":"10613_CR16","doi-asserted-by":"publisher","first-page":"2250042","DOI":"10.1142\/S0218213022500427","volume":"31","author":"T Yao","year":"2022","unstructured":"Yao T, Liu X. Financial time series forecasting: a combinatorial forecasting model based on STOA optimizing VMD. Int J Artif Intell Tools. 2022;31(08):2250042.","journal-title":"Int J Artif Intell Tools"},{"key":"10613_CR17","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1016\/j.asoc.2017.01.015","volume":"54","author":"X Qiu","year":"2017","unstructured":"Qiu X, Ren Y, et al. Empirical mode decomposition based ensemble deep learning for load demand time series forecasting. Appl Soft Comput. 2017;54:246\u201355.","journal-title":"Appl Soft Comput"},{"key":"10613_CR18","doi-asserted-by":"publisher","first-page":"108","DOI":"10.3390\/a10030108","volume":"10","author":"D Wang","year":"2017","unstructured":"Wang D, Yue C, Wei S, Lv J. Performance analysis of four decomposition-ensemble models for one-day-ahead agricultural commodity futures price forecasting. Algorithms. 2017;10:108.","journal-title":"Algorithms"},{"key":"10613_CR19","doi-asserted-by":"publisher","first-page":"129824","DOI":"10.1016\/j.energy.2023.129824","volume":"288","author":"S Parri","year":"2024","unstructured":"Parri S, Teeparthi K, Kosana V. A hybrid methodology using VMD and disentangled features for wind speed forecasting. Energy. 2024;288:129824.","journal-title":"Energy"},{"key":"10613_CR20","doi-asserted-by":"publisher","first-page":"2623","DOI":"10.1016\/j.eneco.2008.05.003","volume":"30","author":"L Yu","year":"2008","unstructured":"Yu L, Wang S, Lai K. Forecasting crude oil price with an EMD-based neural network ensemble learning paradigm. Energy Economics. 2008;30:2623\u201335.","journal-title":"Energy Economics"},{"key":"10613_CR21","doi-asserted-by":"publisher","first-page":"105140","DOI":"10.1016\/j.eneco.2021.105140","volume":"95","author":"Y Li","year":"2021","unstructured":"Li Y, Jiang S, Li X, Wang S. The role of news sentiment in oil futures returns and volatility forecasting: data-decomposition based deep learning approach. Energy Econ. 2021;95:105140.","journal-title":"Energy Econ"},{"key":"10613_CR22","doi-asserted-by":"publisher","first-page":"109723","DOI":"10.1016\/j.asoc.2022.109723","volume":"130","author":"Y Lin","year":"2022","unstructured":"Lin Y, Chen K, Zhang X, Tan B, Lu Q. Forecasting crude oil futures prices using BiLSTM-Attention-CNN model with wavelet transform. Appl Soft Comput. 2022;130:109723.","journal-title":"Appl Soft Comput"},{"key":"10613_CR23","doi-asserted-by":"publisher","first-page":"103602","DOI":"10.1016\/j.resourpol.2023.103602","volume":"83","author":"J Wu","year":"2023","unstructured":"Wu J, Dong J, Wang Z, Hu Y, Dou W. A novel hybrid model based on deep learning and error correction for crude oil futures prices forecast. Resour Policy. 2023;83:103602.","journal-title":"Resour Policy"},{"key":"10613_CR24","doi-asserted-by":"publisher","first-page":"124261","DOI":"10.1016\/j.apenergy.2024.124261","volume":"376","author":"J Liu","year":"2024","unstructured":"Liu J, Zhao X, Luo R, Tao Z. A novel link prediction model for interval-valued crude oil prices based on complex network and multi-source information. Appl Energy. 2024;376:124261.","journal-title":"Appl Energy"},{"key":"10613_CR25","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/j.eneco.2018.02.021","volume":"71","author":"M Wang","year":"2018","unstructured":"Wang M, Tian L, Zhou P. A novel approach for oil price forecasting based on data fluctuation network. Energy Econ. 2018;71:201\u201312.","journal-title":"Energy Econ"},{"key":"10613_CR26","doi-asserted-by":"publisher","first-page":"1103","DOI":"10.3389\/fphy.2022.1029600","volume":"10","author":"Y Hu","year":"2022","unstructured":"Hu Y, Chu C, Wu P, Hu J. A linear time series analysis of carbon price via a complex network approach. Frontiers in Physics. 2022;10:1103.","journal-title":"Frontiers in Physics"},{"key":"10613_CR27","doi-asserted-by":"publisher","first-page":"122830","DOI":"10.1016\/j.physa.2019.122830","volume":"545","author":"H Xu","year":"2020","unstructured":"Xu H, Wang M, Jiang S, Yang W. Carbon price forecasting with complex network and extreme learning machine. Physica A. 2020;545:122830.","journal-title":"Physica A"},{"key":"10613_CR28","doi-asserted-by":"publisher","first-page":"120647","DOI":"10.1016\/j.eswa.2023.120647","volume":"230","author":"S Mao","year":"2023","unstructured":"Mao S, Zeng X. SimVGNets: similarity-based visibility graph networks for carbon price forecasting. Expert Syst Appl. 2023;230:120647.","journal-title":"Expert Syst Appl"},{"issue":"2","key":"10613_CR29","doi-asserted-by":"publisher","first-page":"731","DOI":"10.1016\/j.chaos.2007.01.085","volume":"39","author":"X Yin","year":"2009","unstructured":"Yin X, Yang X, Yang Z. Using the R\/S method to determine the periodicity of time series. Chaos Solitons Fractals. 2009;39(2):731\u201345.","journal-title":"Chaos Solitons Fractals"},{"key":"10613_CR30","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1016\/j.neunet.2019.05.018","volume":"117","author":"L Anghinoni","year":"2019","unstructured":"Anghinoni L, Zhao L, Ji D, et al. Time series trend detection and forecasting using complex network topology analysis. Neural Netw. 2019;117:295\u2013306.","journal-title":"Neural Netw"},{"key":"10613_CR31","doi-asserted-by":"publisher","first-page":"4972","DOI":"10.1073\/pnas.0709247105","volume":"105","author":"L Lacasa","year":"2008","unstructured":"Lacasa L, Luque B, Ballesteros F, Luque J, Nu\u00f1o J. From time series to complex networks: the visibility graph. Proc Natl Acad Sci U S A. 2008;105:4972\u20135.","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"4","key":"10613_CR32","doi-asserted-by":"publisher","first-page":"1281","DOI":"10.1109\/TFUZZ.2022.3198177","volume":"31","author":"Y Hu","year":"2023","unstructured":"Hu Y, Xiao F. Time-series forecasting based on fuzzy cognitive visibility graph and weighted multisubgraph similarity. IEEE Trans Fuzzy Syst. 2023;31(4):1281\u201393.","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"10613_CR33","doi-asserted-by":"publisher","first-page":"116502","DOI":"10.1016\/j.eswa.2022.116502","volume":"194","author":"H Li","year":"2022","unstructured":"Li H, Jia R, Wan X. Time series classification based on complex network. Expert Syst Appl. 2022;194:116502.","journal-title":"Expert Syst Appl"},{"key":"10613_CR34","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/j.chaos.2018.07.039","volume":"117","author":"P Xu","year":"2018","unstructured":"Xu P, Zhang R, Deng Y. A novel visibility graph transformation of time series into weighted networks. Chaos Solitons Fractals. 2018;117:201\u20138.","journal-title":"Chaos Solitons Fractals"},{"key":"10613_CR35","doi-asserted-by":"publisher","first-page":"106162","DOI":"10.1016\/j.eneco.2022.106162","volume":"112","author":"M Wang","year":"2022","unstructured":"Wang M, Zhu M, Tian L. A novel framework for carbon price forecasting with uncertainties. Energy Econ. 2022;112:106162.","journal-title":"Energy Econ"},{"key":"10613_CR36","doi-asserted-by":"publisher","first-page":"683","DOI":"10.1177\/0165551516664039","volume":"43","author":"C Yu","year":"2017","unstructured":"Yu C, Zhao X, An L, Lin X. Similarity-based link prediction in social networks: a path and node combined approach. J Inf Sci. 2017;43:683\u201395.","journal-title":"J Inf Sci"},{"issue":"6","key":"10613_CR37","doi-asserted-by":"publisher","first-page":"1150","DOI":"10.1016\/j.physa.2010.11.027","volume":"390","author":"L L\u00fc","year":"2011","unstructured":"L\u00fc L, Zhou T. Link prediction in complex networks: a survey. Phys A. 2011;390(6):1150\u201370.","journal-title":"Phys A"},{"issue":"8","key":"10613_CR38","doi-asserted-by":"publisher","first-page":"5375","DOI":"10.1016\/j.jksuci.2021.05.006","volume":"34","author":"K Berahmand","year":"2022","unstructured":"Berahmand K, Nasiri E, Forouzandeh S, Li Y. A preference random walk algorithm for link prediction through mutual influence nodes in complex networks. J King Saud Univ - Comput Inf Sci. 2022;34(8):5375\u201387.","journal-title":"J King Saud Univ - Comput Inf Sci"},{"key":"10613_CR39","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","volume":"62","author":"K Dragomiretskiy","year":"2014","unstructured":"Dragomiretskiy K, Zosso D. Variational mode decomposition. IEEE Trans Signal Process. 2014;62:531\u201344.","journal-title":"IEEE Trans Signal Process"},{"key":"10613_CR40","doi-asserted-by":"publisher","first-page":"40220","DOI":"10.1109\/ACCESS.2019.2906268","volume":"7","author":"S Mao","year":"2019","unstructured":"Mao S, Xiao F. Time series forecasting based on complex network analysis. IEEE Access. 2019;7:40220\u20139.","journal-title":"IEEE Access"},{"key":"10613_CR41","doi-asserted-by":"publisher","first-page":"127029","DOI":"10.1016\/j.physa.2022.127029","volume":"594","author":"Y Hu","year":"2022","unstructured":"Hu Y, Xiao F. A novel method for forecasting time series based on directed visibility graph and improved random walk. Phys A Stat Mech Appl. 2022;594:127029.","journal-title":"Phys A Stat Mech Appl"},{"key":"10613_CR42","doi-asserted-by":"publisher","first-page":"124261","DOI":"10.1016\/j.apenergy.2024.124261","volume":"376","author":"J Liu","year":"2024","unstructured":"Liu J, Zhao X, Luo R, et al. A novel link prediction model for interval-valued crude oil prices based on complex network and multi-source information. Appl Energy. 2024;376:124261.","journal-title":"Appl Energy"}],"container-title":["Cognitive Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12559-026-10613-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12559-026-10613-7","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12559-026-10613-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T05:10:00Z","timestamp":1781241000000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12559-026-10613-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,12]]},"references-count":42,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,12]]}},"alternative-id":["10613"],"URL":"https:\/\/doi.org\/10.1007\/s12559-026-10613-7","relation":{},"ISSN":["1866-9956","1866-9964"],"issn-type":[{"value":"1866-9956","type":"print"},{"value":"1866-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,12]]},"assertion":[{"value":"20 July 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 June 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 June 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"68"}}