{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T18:14:42Z","timestamp":1777486482557,"version":"3.51.4"},"reference-count":37,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T00:00:00Z","timestamp":1755820800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This research evaluates the suitability of Graph Convolutional Networks (GCN) and Graph Attention Networks (GAT) for improving financial return predictions across 15 major worldwide stock indices. The proposed method uses graph modeling to represent financial index relationships which enables the detection of symmetric market dependencies including mutual spillover effects and bidirectional influence patterns. The symmetric network structures become most important during financial instability because market interdependencies strengthen at such times. The evaluation process compares these models against XGBoost and Multi-Layer Perceptron (MLP) and Support Vector Machine (SVM) traditional forecasting approaches. The results of 30 time-series cross-validation experiments show that GNN models produce lower RMSE and MAE values, especially during financial crises and recovery phases and volatile market periods. The models show reduced advantages when markets remain stable. The research demonstrates that graph-based forecasting models which incorporate symmetry effectively detect complex financial relationships which leads to important implications for investment strategies and financial risk management and global economic forecasting.<\/jats:p>","DOI":"10.3390\/sym17091372","type":"journal-article","created":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T07:41:45Z","timestamp":1755848505000},"page":"1372","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Symmetry-Aware Graph Neural Approaches for Data-Efficient Return Prediction in International Financial Market Indices"],"prefix":"10.3390","volume":"17","author":[{"given":"Tae Kyoung","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Industrial and Management Systems Engineering, Kyung Hee University, Yongin 17104, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2596-7368","authenticated-orcid":false,"given":"Insu","family":"Choi","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8385-9598","authenticated-orcid":false,"given":"Woo Chang","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,22]]},"reference":[{"key":"ref_1","unstructured":"Box, G.E.P., Jenkins, G.M., Reinsel, G.C., and Ljung, G.M. 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