{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:02:11Z","timestamp":1760238131482,"version":"build-2065373602"},"reference-count":55,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,9]],"date-time":"2022-06-09T00:00:00Z","timestamp":1654732800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11671266","71673315","71850008","72003110","11931019"],"award-info":[{"award-number":["11671266","71673315","71850008","72003110","11931019"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The correlation-based network is a powerful tool to reveal the influential mechanisms and relations in stock markets. However, current methods for developing network models are dominantly based on the pairwise relationship of positive correlations. This work proposes a new approach for developing stock relationship networks by using the linear relationship model with LASSO to explore negative correlations under a systemic framework. The developed model not only preserves positive links with statistical significance but also includes link directions and negative correlations. We also introduce blends cliques with the balance theory to investigate the consistency properties of the developed networks. The ASX 200 stock data with 194 stocks are applied to evaluate the effectiveness of our proposed method. Results suggest that the developed networks not only are highly consistent with the correlation coefficient in terms of positive or negative correlations but also provide influence directions in stock markets.<\/jats:p>","DOI":"10.3390\/e24060808","type":"journal-article","created":{"date-parts":[[2022,6,10]],"date-time":"2022-06-10T00:22:39Z","timestamp":1654820559000},"page":"808","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Linear Relationship Model with LASSO for Studying Stock Networks"],"prefix":"10.3390","volume":"24","author":[{"given":"Muzi","family":"Chen","sequence":"first","affiliation":[{"name":"School of Management Science and Engineering, Central University of Finance and Economics, Beijing 102206, China"}]},{"given":"Hongjiong","family":"Tian","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2186-808X","authenticated-orcid":false,"given":"Boyao","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Banking and Finance, University of International Business and Economics, Beijing 100029, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6191-0209","authenticated-orcid":false,"given":"Tianhai","family":"Tian","sequence":"additional","affiliation":[{"name":"School of Mathematics, Monash University, Clayton, VIC 3800, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1126\/science.aah3449","article-title":"Network analytics in the age of big data","volume":"353","year":"2016","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1243089","DOI":"10.1126\/science.1243089","article-title":"Economics in the age of big data","volume":"346","author":"Einav","year":"2014","journal-title":"Science"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1126\/science.aaa8415","article-title":"Machine learning: Trends, perspectives, and prospects","volume":"349","author":"Jordan","year":"2015","journal-title":"Science"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1126\/science.1215842","article-title":"Identifying influential and susceptible members of social networks","volume":"337","author":"Aral","year":"2012","journal-title":"Science"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1038\/nature09659","article-title":"Systemic risk in banking ecosystems","volume":"469","author":"Haldane","year":"2011","journal-title":"Nature"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1581","DOI":"10.1016\/j.cell.2018.05.015","article-title":"Next-generation machine learning for biological networks","volume":"173","author":"Camacho","year":"2018","journal-title":"Cell"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"198301","DOI":"10.1103\/PhysRevLett.119.198301","article-title":"Closed-loop control of complex networks: A trade-off between time and energy","volume":"119","author":"Sun","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"048301","DOI":"10.1103\/PhysRevLett.118.048301","article-title":"Vulnerability and cosusceptibility determine the size of network cascades","volume":"118","author":"Yang","year":"2017","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1038\/s42005-019-0144-6","article-title":"Extreme risk induced by communities in interdependent networks","volume":"2","author":"Sun","year":"2019","journal-title":"Commun. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1581","DOI":"10.1080\/01605682.2019.1595193","article-title":"Computational approaches and data analytics in financial services: A literature review","volume":"70","author":"Andriosopoulos","year":"2019","journal-title":"J. Oper. Res. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s41060-021-00306-9","article-title":"A survey of the application of graph-based approaches in stock market analysis and prediction","volume":"14","author":"Saha","year":"2022","journal-title":"Int. J. Data Sci. Anal."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s100510050929","article-title":"Hierarchical structure in financial markets","volume":"11","author":"Mantegna","year":"1999","journal-title":"Eur. Phys. J. B-Condens. Matter Complex Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"10421","DOI":"10.1073\/pnas.0500298102","article-title":"A tool for filtering information in complex systems","volume":"102","author":"Tumminello","year":"2005","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1140\/epjb\/e2006-00414-4","article-title":"Correlation based networks of equity returns sampled at different time horizons","volume":"55","author":"Tumminello","year":"2007","journal-title":"Eur. Phys. J. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1016\/j.physa.2014.01.011","article-title":"Cointegration analysis and influence rank\u2014A network approach to global stock markets","volume":"400","author":"Yang","year":"2014","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Kenett, D.Y., Tumminello, M., Madi, A., Gur-Gershgoren, G., Mantegna, R.N., and Ben-Jacob, E. (2010). Dominating clasp of the financial sector revealed by partial correlation analysis of the stock market. PLoS ONE, 5.","DOI":"10.1371\/journal.pone.0015032"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"S241","DOI":"10.1016\/j.jbankfin.2015.08.034","article-title":"Connecting the dots: Econometric methods for uncovering networks with an application to the Australian financial institutions","volume":"61","author":"Anufriev","year":"2015","journal-title":"J. Bank. Financ."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1080\/14697688.2014.946660","article-title":"Partial correlation analysis: Applications for financial markets","volume":"15","author":"Kenett","year":"2015","journal-title":"Quant. Financ."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/j.jfineco.2011.12.010","article-title":"Econometric measures of connectedness and systemic risk in the finance and insurance sectors","volume":"104","author":"Billio","year":"2012","journal-title":"J. Financ. Econ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"10646","DOI":"10.1073\/pnas.1819449116","article-title":"Hidden interactions in financial markets","volume":"116","author":"Stavroglou","year":"2019","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Guo, X., Zhang, H., and Tian, T. (2018). Development of stock correlation networks using mutual information and financial big data. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0195941"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Yan, Y., Wu, Y., Tian, T., and Zhang, H. (2020). Development of Stock Networks Using Part Mutual Information and Australian Stock Market Data. Entropy, 22.","DOI":"10.3390\/e22070773"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Sharma, C., and Habib, A. (2019). Mutual information based stock networks and portfolio selection for intraday traders using high frequency data: An Indian market case study. PLoS ONE, 14.","DOI":"10.1371\/journal.pone.0221910"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Chen, M., Wang, Y., Wu, B., and Huang, D. (2021). Dynamic analyses of contagion risk and module evolution on the SSE a-shares market based on minimum information entropy. Entropy, 23.","DOI":"10.2139\/ssrn.3799784"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"17618","DOI":"10.1038\/s41598-021-97100-1","article-title":"Structure and dynamics of financial networks by feature ranking method","volume":"11","author":"Rakib","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Karkowska, R., and Urjasz, S. (2022). Linear and nonlinear effects in connectedness structure: Comparison between european stock markets. Entropy, 24.","DOI":"10.3390\/e24020303"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1002\/asmb.2644","article-title":"Clustering high-frequency financial time series based on information theory","volume":"38","author":"Liu","year":"2022","journal-title":"Appl. Stoch. Molels Bus Ind."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Libman, D., Ariel, G., Schaps, M., and Haber, S. (2022). Mutual information between order book layers. Entropy, 24.","DOI":"10.3390\/e24030343"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Wang, Z., Shi, G., Shang, M., and Zhang, Y. (2021). The stock market model with delayed information impact from a socioeconomic view. Entropy, 23.","DOI":"10.3390\/e23070893"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Tang, L., Lu, B., and Tian, T. (2021). Spatial correlation network and regional differences for the development of digital economy in China. Entropy, 23.","DOI":"10.3390\/e23121575"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2050018","DOI":"10.1142\/S0219477520500182","article-title":"An effective stock classification method via MDS based on modified mutual information distance","volume":"19","author":"Jiang","year":"2020","journal-title":"Fluct. Noise Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.1016\/j.physa.2019.04.128","article-title":"Network analysis of the Chinese stock market during the turbulence of 2015?2016 using log-returns, volumes and mutual information","volume":"523","author":"Dong","year":"2019","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1238\/Physica.Topical.106a00048","article-title":"Asset trees and asset graphs in financial markets","volume":"2003","author":"Onnela","year":"2003","journal-title":"Phys. Scr."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1016\/j.jempfin.2010.04.008","article-title":"A network perspective of the stock market","volume":"17","author":"Chi","year":"2010","journal-title":"J. Empir. Financ."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1007\/s10614-015-9481-z","article-title":"Analysis of correlation based networks representing DAX 30 stock price returns","volume":"47","author":"Birch","year":"2016","journal-title":"Comput. Econ."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"48005","DOI":"10.1209\/0295-5075\/86\/48005","article-title":"Cross-correlation in financial dynamics","volume":"86","author":"Shen","year":"2009","journal-title":"EPL (Europhys. Lett.)"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1750018","DOI":"10.1142\/S0219477517500183","article-title":"Market correlation structure changes around the great crash: A random matrix theory analysis of the chinese stock market","volume":"16","author":"Han","year":"2017","journal-title":"Fluct. Noise Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1016\/j.physa.2013.08.053","article-title":"Stock network stability in times of crisis","volume":"393","author":"Heiberger","year":"2014","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"126421","DOI":"10.1016\/j.physa.2021.126421","article-title":"Multi-likelihood methods for developing relationship networks using stock market data","volume":"585","author":"Guo","year":"2022","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1114","DOI":"10.1038\/nbt.2018","article-title":"In silico feedback for in vivo regulation of a gene expression circuit","volume":"29","author":"Summers","year":"2011","journal-title":"Nat. Biotechnol."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"12546","DOI":"10.1038\/ncomms12546","article-title":"Automated optogenetic feedback control for precise and robust regulation of gene expression and cell growth","volume":"7","author":"Rullan","year":"2016","journal-title":"Nat. Commun."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1436","DOI":"10.1214\/009053606000000281","article-title":"High-dimensional graphs and variable selection with the lasso","volume":"34","author":"Meinshausen","year":"2006","journal-title":"Ann. Stat."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1214\/15-STS527","article-title":"High-dimensional inference: Confidence intervals, p-values and r-software hdi","volume":"30","author":"Dezeure","year":"2015","journal-title":"Stat. Sci."},{"key":"ref_44","unstructured":"Xu, H., Caramanis, C., and Mannor, S. (2009). Robust regression and lasso. Advances in Neural Information Processing Systems, MIT Press."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1567","DOI":"10.1214\/07-AOS520","article-title":"The sparsity and bias of the lasso selection in high-dimensional linear regression","volume":"36","author":"Zhang","year":"2008","journal-title":"Ann. Stat."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"7046","DOI":"10.1016\/j.eswa.2015.05.013","article-title":"Evaluating multiple classifiers for stock price direction prediction","volume":"42","author":"Ballings","year":"2015","journal-title":"Expert Syst. Appl."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"996","DOI":"10.1016\/j.ijforecast.2014.03.016","article-title":"Forecasting macroeconomic time series: LASSO-based approaches and their forecast combinations with dynamic factor models","volume":"30","author":"Li","year":"2014","journal-title":"Int. J. Forecast."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/j.frl.2018.03.016","article-title":"On the determinants of bitcoin returns: A LASSO approach","volume":"27","author":"Panagiotidis","year":"2018","journal-title":"Financ. Res. Lett."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Ogutu, J.O., Schulz-Streeck, T., and Piepho, H.P. (2012). Genomic selection using regularized linear regression models: Ridge regression, lasso, elastic net and their extensions. BMC Proc., 6.","DOI":"10.1186\/1753-6561-6-S2-S10"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1348","DOI":"10.1198\/016214501753382273","article-title":"Variable selection via nonconcave penalized likelihood and its oracle properties","volume":"96","author":"Fan","year":"2001","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1418","DOI":"10.1198\/016214506000000735","article-title":"The adaptive lasso and its oracle properties","volume":"101","author":"Zou","year":"2006","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Wasserman, S., and Faust, K. (1994). Social Network Analysis: Methods and Applications, Cambridge University Press.","DOI":"10.1017\/CBO9780511815478"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.jempfin.2016.06.003","article-title":"A network approach to portfolio selection","volume":"38","author":"Peralta","year":"2016","journal-title":"J. Empir. Financ. Part A"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1016\/j.physa.2018.10.014","article-title":"Portfolio optimization based on network topology","volume":"515","author":"Li","year":"2019","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"101503","DOI":"10.1016\/j.najef.2021.101503","article-title":"Network-augmented time-varying parametric portfolio selection: Evidence from the Chinese stock market","volume":"58","author":"Xu","year":"2021","journal-title":"N. Am. J. Econ. Financ."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/6\/808\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:27:09Z","timestamp":1760138829000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/6\/808"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,9]]},"references-count":55,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["e24060808"],"URL":"https:\/\/doi.org\/10.3390\/e24060808","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,6,9]]}}}