{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T15:43:20Z","timestamp":1779291800379,"version":"3.51.4"},"reference-count":56,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,17]],"date-time":"2025-08-17T00:00:00Z","timestamp":1755388800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science and Technology Major Project undertaken by the Shenzhen Technology and Innovation Council","award":["CJGJZD20220517141800002"],"award-info":[{"award-number":["CJGJZD20220517141800002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Accurately predicting stock prices is crucial for investment and risk management, but the non-stationarity of the financial market and the complex correlations among stocks pose challenges to traditional models (ARIMA, LSTM, XGBoost), resulting in difficulties in effectively capturing dynamic patterns and limited prediction accuracy. To this end, this paper proposes the Financial Spatio-Temporal Graph Attention Network (FSTGAT), with the following core innovations: temporal modelling through gated causal convolution to avoid future information leakage and capture long- and short-term fluctuations; enhanced spatial correlation learning by adopting the Dynamic Graph Attention Mechanism (GATv2) that incorporates industry information; designing the Multiple-Input-Multiple-Output (MIMO) architecture of industry grouping for the simultaneous learning of intra-group synergistic and inter-group influence; symmetrically fusing spatio-temporal modules to construct a hierarchical feature extraction framework. Experiments in the commercial banking and metals sectors of the New York Stock Exchange (NYSE) show that FSTGAT significantly outperforms the benchmark model, especially in high-volatility scenarios, where the prediction error is reduced by 45\u201369%, and can accurately capture price turning points. This study confirms the potential of graph neural networks to model the structure of financial interconnections, providing an effective tool for stock forecasting in non-stationary markets, and its forecasting accuracy and industry correlation capturing ability can support portfolio optimization, risk management improvement and supply chain decision guidance.<\/jats:p>","DOI":"10.3390\/sym17081344","type":"journal-article","created":{"date-parts":[[2025,8,18]],"date-time":"2025-08-18T07:53:12Z","timestamp":1755503592000},"page":"1344","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["FSTGAT: Financial Spatio-Temporal Graph Attention Network for Non-Stationary Financial Systems and Its Application in Stock Price Prediction"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-5258-4318","authenticated-orcid":false,"given":"Ze-Lin","family":"Wei","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR 999077, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-7779-7824","authenticated-orcid":false,"given":"Hong-Yu","family":"An","sequence":"additional","affiliation":[{"name":"Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-2530-981X","authenticated-orcid":false,"given":"Yao","family":"Yao","sequence":"additional","affiliation":[{"name":"Shenzhen Nanshan Experimental Education Group, OCT Senior High School, Shenzhen 518058, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-6512-2125","authenticated-orcid":false,"given":"Wei-Cong","family":"Su","sequence":"additional","affiliation":[{"name":"Shenzhen Kaihong Digital Industry Development Co., Ltd., Shenzhen 518000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4431-7857","authenticated-orcid":false,"given":"Guo","family":"Li","sequence":"additional","affiliation":[{"name":"Shenzhen Kaihong Digital Industry Development Co., Ltd., Shenzhen 518000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3295-0388","authenticated-orcid":false,"family":"Saifullah","sequence":"additional","affiliation":[{"name":"Shenzhen Kaihong Digital Industry Development Co., Ltd., Shenzhen 518000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-0677-8902","authenticated-orcid":false,"given":"Bi-Feng","family":"Sun","sequence":"additional","affiliation":[{"name":"Shenzhen Kaihong Digital Industry Development Co., Ltd., Shenzhen 518000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0950-4558","authenticated-orcid":false,"given":"Mu-Jiang-Shan","family":"Wang","sequence":"additional","affiliation":[{"name":"Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China"},{"name":"Shenzhen Kaihong Digital Industry Development Co., Ltd., Shenzhen 518000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"00368504241236557","DOI":"10.1177\/00368504241236557","article-title":"A bibliometric literature review of stock price forecasting: From statistical model to deep learning approach","volume":"107","author":"Vuong","year":"2024","journal-title":"Sci. Prog."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Sonkavde, G., Dharrao, D.S., Bongale, A.M., Deokate, S.T., Doreswamy, D., and Bhat, S.K. (2023). Forecasting stock market prices using machine learning and deep learning models: A systematic review, performance analysis and discussion of implications. Int. J. Financ. Stud., 11.","DOI":"10.3390\/ijfs11030094"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bhattacharjee, I., and Bhattacharja, P. (2019, January 20\u201322). Stock price prediction: A comparative study between traditional statistical approach and machine learning approach. Proceedings of the 2019 4th International Conference on Electrical Information and Communication Technology (EICT), Khulna, Bangladesh.","DOI":"10.1109\/EICT48899.2019.9068850"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"121899","DOI":"10.1016\/j.eswa.2023.121899","article-title":"Attention based adaptive spatial\u2013temporal hypergraph convolutional networks for stock price trend prediction","volume":"238","author":"Su","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1007\/s11831-019-09344-w","article-title":"A survey of deep learning and its applications: A new paradigm to machine learning","volume":"27","author":"Dargan","year":"2020","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1609","DOI":"10.1007\/s00521-019-04212-x","article-title":"Stock price prediction based on deep neural networks","volume":"32","author":"Yu","year":"2020","journal-title":"Neural Comput. Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"132306","DOI":"10.1016\/j.physd.2019.132306","article-title":"Fundamentals of recurrent neural network (RNN) and long short-term memory (LSTM) network","volume":"404","author":"Sherstinsky","year":"2020","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1235","DOI":"10.1162\/neco_a_01199","article-title":"A review of recurrent neural networks: LSTM cells and network architectures","volume":"31","author":"Yu","year":"2019","journal-title":"Neural Comput."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1007\/s13042-019-01041-1","article-title":"Study on the prediction of stock price based on the associated network model of LSTM","volume":"11","author":"Ding","year":"2020","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3696411","article-title":"A Systematic Review on Graph Neural Network-based Methods for Stock Market Forecasting","volume":"57","author":"Patel","year":"2024","journal-title":"ACM Comput. Surv."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wang, J., Zhang, S., Xiao, Y., and Song, R. (2021). A review on graph neural network methods in financial applications. arXiv.","DOI":"10.6339\/22-JDS1047"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Yu, B., Yin, H., and Zhu, Z. (2017). Spatio-temporal graph convolutional networks: A deep learning framework for traffic forecasting. arXiv.","DOI":"10.24963\/ijcai.2018\/505"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1002\/(SICI)1099-131X(199705)16:3<147::AID-FOR652>3.0.CO;2-X","article-title":"ARMA models and the Box\u2013Jenkins methodology","volume":"16","author":"Makridakis","year":"1997","journal-title":"J. Forecast."},{"key":"ref_14","first-page":"2395","article-title":"Stock price prediction using ARIMA model","volume":"8","author":"Ganesan","year":"2021","journal-title":"Int. Res. J. Eng. Technol. (IRJET)"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Ariyo, A.A., Adewumi, A.O., and Ayo, C.K. (2014, January 26\u201328). Stock price prediction using the ARIMA model. Proceedings of the 2014 UKSim-AMSS 16th International Conference on Computer Modelling and Simulation, Cambridge, UK.","DOI":"10.1109\/UKSim.2014.67"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"987","DOI":"10.2307\/1912773","article-title":"Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation","volume":"50","author":"Engle","year":"1982","journal-title":"Econometrica"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/07474938608800095","article-title":"Modelling the persistence of conditional variances","volume":"5","author":"Engle","year":"1986","journal-title":"Econom. Rev."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/S0305-0483(01)00026-3","article-title":"Application of support vector machines in financial time series forecasting","volume":"29","author":"Tay","year":"2001","journal-title":"Omega"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Chen, T., and Guestrin, C. (2016, January 13\u201317). XGBoost: A scalable tree boosting system. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/2939672.2939785"},{"key":"ref_21","first-page":"3149","article-title":"LightGBM: A highly efficient gradient boosting decision tree","volume":"30","author":"Ke","year":"2017","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long short-term memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"654","DOI":"10.1016\/j.ejor.2017.11.054","article-title":"Deep learning with long short-term memory networks for financial market predictions","volume":"270","author":"Fischer","year":"2018","journal-title":"Eur. J. Oper. Res."},{"key":"ref_24","first-page":"2","article-title":"LSTM Neural Network with Emotional Analysis for Prediction of Stock Price","volume":"25","author":"Zhuge","year":"2017","journal-title":"Eng. Lett."},{"key":"ref_25","unstructured":"Bai, S., Kolter, J.Z., and Koltun, V. (2018). An empirical evaluation of generic convolutional and recurrent networks for sequence modeling. arXiv."},{"key":"ref_26","unstructured":"Van Den Oord, A., Dieleman, S., Zen, H., Simonyan, K., Vinyals, O., Graves, A., Kalchbrenner, N., Senior, A., and Kavukcuoglu, K. (2016). Wavenet: A generative model for raw audio. arXiv."},{"key":"ref_27","unstructured":"Kipf, T.N., and Welling, M. (2016). Semi-supervised classification with graph convolutional networks. arXiv."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"797","DOI":"10.5267\/j.msl.2015.7.003","article-title":"Stocks\u2019 pricing dynamics and behavioral finance: A review","volume":"5","author":"Sinha","year":"2015","journal-title":"Manag. Sci. Lett."},{"key":"ref_29","unstructured":"Veli\u010dkovi\u0107, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., and Bengio, Y. (2017). Graph attention networks. arXiv."},{"key":"ref_30","unstructured":"Brody, S., Alon, U., and Yahav, E. (2021). How attentive are graph attention networks?. arXiv."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.patcog.2019.01.006","article-title":"Wider or deeper: Revisiting the resnet model for visual recognition","volume":"90","author":"Wu","year":"2019","journal-title":"Pattern Recognit."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Sawhney, R., Agarwal, S., Wadhwa, A., Derr, T., and Shah, R.R. (2021, January 2\u20139). Stock Selection via Spatiotemporal Hypergraph Attention Network: A Learning to Rank Approach. Proceedings of the AAAI Conference on Artificial Intelligence, Virtual Event. Number 1.","DOI":"10.1609\/aaai.v35i1.16127"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"117123","DOI":"10.1016\/j.eswa.2022.117123","article-title":"BiCuDNNLSTM-1dCNN\u2014A hybrid deep learning-based predictive model for stock price prediction","volume":"202","author":"Kanwal","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Jin, Y. (2024, January 20\u201322). GraphCNNpred: A stock market indices prediction using a Graph based deep learning system. Proceedings of the 2024 2nd International Conference on Artificial Intelligence, Systems and Network Security, Mianyang China.","DOI":"10.1145\/3714334.3714364"},{"key":"ref_35","unstructured":"Liu, C., and Paterlini, S. (2023). Stock price prediction using temporal graph model with value chain data. arXiv."},{"key":"ref_36","unstructured":"Yan, W., and Tan, Y. (2024). TCGPN: Temporal-Correlation Graph Pre-trained Network for Stock Forecasting. arXiv."},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Feng, R., Jiang, S., Liang, X., and Xia, M. (2025). STGAT: Spatial\u2013Temporal Graph Attention Neural Network for Stock Prediction. Appl. Sci., 15.","DOI":"10.3390\/app15084315"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"127","DOI":"10.4236\/ajcm.2017.72011","article-title":"The tightly super 3-extra connectivity and diagnosability of locally twisted cubes","volume":"7","author":"Wang","year":"2017","journal-title":"Am. J. Comput. Math."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Zhou, G., and Wang, R.-F. (2025). The Heterogeneous Network Community Detection Model Based on Self-Attention. Symmetry, 17.","DOI":"10.3390\/sym17030432"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1051\/ita\/2017008","article-title":"The connectivity and nature diagnosability of expanded k-ary n-cubes","volume":"51","author":"Wang","year":"2017","journal-title":"RAIRO-Theor. Inform. Appl.-Inform. Th\u00e9or. Appl."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Wang, R.-F., Qu, H.-R., and Su, W.-H. (2025). From Sensors to Insights: Technological Trends in Image-Based High-Throughput Plant Phenotyping. Smart Agric. Technol., 101257.","DOI":"10.1016\/j.atech.2025.101257"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2040004","DOI":"10.1142\/S0129626420400046","article-title":"Connectivity and diagnosability of leaf-sort graphs","volume":"30","author":"Wang","year":"2020","journal-title":"Parallel Process. Lett."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Yang, Z.X., Li, Y., Wang, R.F., Hu, P., and Su, W.H. (2025). Deep Learning in Multimodal Fusion for Sustainable Plant Care: A Comprehensive Review. Sustainability, 17.","DOI":"10.3390\/su17125255"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Cheng, P., Xia, M., Wang, D., Lin, H., and Zhao, Z. (2025). Transformer Self-Attention Change Detection Network with Frozen Parameters. Appl. Sci., 15.","DOI":"10.3390\/app15063349"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Yang, Z.Y., Xia, W.K., Chu, H.Q., Su, W.H., Wang, R.F., and Wang, H. (2025). A comprehensive review of deep learning applications in cotton industry: From field monitoring to smart processing. Plants, 14.","DOI":"10.3390\/plants14101481"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"115027","DOI":"10.1016\/j.tcs.2024.115027","article-title":"G-good-neighbor diagnosability under the modified comparison model for multiprocessor systems","volume":"1028","author":"Wang","year":"2025","journal-title":"Theor. Comput. Sci."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Wang, Z., Zhang, H.W., Dai, Y.Q., Cui, K., Wang, H., Chee, P.W., and Wang, R.F. (2025). Resource-Efficient Cotton Network: A Lightweight Deep Learning Framework for Cotton Disease and Pest Classification. Plants, 14.","DOI":"10.3390\/plants14132082"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Wang, M., Xu, S., Jiang, J., Xiang, D., and Hsieh, S.-Y. (2025). Global Reliable Diagnosis of Networks Based on Self-Comparative Diagnosis Model and g-Good-Neighbor Property. J. Comput. Syst. Sci., 103698.","DOI":"10.1016\/j.jcss.2025.103698"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Qin, Y.M., Tu, Y.H., Li, T., Ni, Y., Wang, R.F., and Wang, H. (2025). Deep Learning for sustainable agriculture: A systematic review on applications in lettuce cultivation. Sustainability, 17.","DOI":"10.3390\/su17073190"},{"key":"ref_50","unstructured":"West, D.B. (2001). Introduction to Graph Theory, Prentice Hall."},{"key":"ref_51","unstructured":"Wu, J. (2017). Introduction to Convolutional Neural Networks, National Key Lab for Novel Software Technology, Nanjing University."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Nauta, M., Bucur, D., and Seifert, C. (2019). Causal discovery with attention-based convolutional neural networks. Mach. Learn. Knowl. Extr., 1.","DOI":"10.3390\/make1010019"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1007\/s11633-016-1006-2","article-title":"Minimal gated unit for recurrent neural networks","volume":"13","author":"Zhou","year":"2016","journal-title":"Int. J. Autom. Comput."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"237","DOI":"10.32604\/csse.2022.017685","article-title":"Stock-Price Forecasting Based on XGBoost and LSTM","volume":"40","author":"Vuong","year":"2022","journal-title":"Comput. Syst. Sci. Eng."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Ozili, P.K. (2024). Causes and consequences of the 2023 banking crisis. Governance and Policy Transformations in Central Banking, IGI Global Scientific Publishing.","DOI":"10.4018\/979-8-3693-0835-6.ch006"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"126430","DOI":"10.1016\/j.eswa.2025.126430","article-title":"Optimizing portfolio selection through stock ranking and matching: A reinforcement learning approach","volume":"269","author":"Alzaman","year":"2025","journal-title":"Expert Syst. Appl."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1344\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:29:34Z","timestamp":1760034574000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1344"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,17]]},"references-count":56,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["sym17081344"],"URL":"https:\/\/doi.org\/10.3390\/sym17081344","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,17]]}}}