Networks of Stock Prices in the Capital Market

Situngkir, Hokky and Muhammad Aldy, Hasan (2026): Networks of Stock Prices in the Capital Market. Published in: BFI Working Paper Series No. WP-06-2026

Abstract

Thecollectivemovementofstockpricesharborscomplexinterdependenciesthatareconventionally simplified only through a linear lens. This paper explores structural network representations in the Indonesian capital market by testing the limits of Pearson correlation and Mutual Information (MI) in unveiling the spectral dynamics of the market. Across 2,328 rolling observation windows from 2015 to 2025, we examine 24 methodological configurations that combine three dependency estimators (Pearson, MI adaptive binning, and MI-kNN), two graph filtering schemes (Minimum Spanning Tree/MST and Planar Maximally Filtered Graph/PMFG), and four community decoders. The empirical results unveil a fundamental reality: topological richness does not always resonate with sectoral classification precision. The Pearson, MST, and Infomap configuration is shown to remain the most robust foundation for recovering conventional sectoral taxonomy. Nevertheless, when deeper observation demands the exposition of local structures and the weave of heterogeneous communities, the architectural relaxation through PMFG demonstrates its superiority. In the realm of residual information detection, MI adaptive binning appears far more proportional than kNN; histogram-based regularization successfully tames empirical noise without sweeping away traces of non-linear dependency. Ultimately, the synergy of MI and PMFG is not positioned to dethrone the dominance of linear correlation, but ratherto provide an essenti alanalytical lens for excavating hidden economic sub-structures—such as the cohesion of commodity regimes—that have long transcended the rigid boundaries of the market’s formal sectors.

• Item Type: MPRA Paper
• Language: English
• Keywords: Econophysics; stock prices; Minimum Spanning Tree (MST); Planar Maximally Filtered Graph (PMFG); Mutual Information; community detection; financial networks
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling; G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions; G - Financial Economics > G2 - Financial Institutions and Services > G28 - Government Policy and Regulation; M - Business Administration and Business Economics ; Marketing ; Accounting ; Personnel Economics > M0 - General

References

[1] R. N. Mantegna, "Hierarchical structure in financial markets," European Physical Journal B, vol. 11, no. 1, pp. 193-197, 1999.

[2] Situngkir, H. & Surya, Y. (2005). "On Stock Market Dynamics through Ultrametricity of Minimum Spanning Tree". BFI Working Paper Series WPH2005.

[3] Situngkir, H. (2015). "On Capturing the Spreading Dynamics over Trading Prices in the Market". BFI Working Paper Series WP-5-2015. arXiv:1510.04690

[4] M. Tumminello, T. Aste, T. Di Matteo, & R. N. Mantegna, "A tool for filtering information in complex systems," Proceedings of the National Academy of Sciences, vol. 102, no. 30, pp. 10421- 10426, 2005.

[5] A. Kraskov, H. Stögbauer, & P. Grassberger, "Estimating mutual information," Physical Review E, vol. 69, 066138, 2004. 11

[6] N.X.Vinh, J.Epps, &J.Bailey, "InformationTheoreticMeasuresforClusteringsComparison: Vari- ants, Properties, Normalization and Correction for Chance," Journal of Machine Learning Research, vol. 11, pp. 2837-2854, 2010.

[7] A. Clauset, M. E. J. Newman, & C. Moore, "Finding community structure in very large networks," Physical Review E, vol. 70, 066111, 2004.

[8] M. E. J. Newman, "Finding community structure in networks using the eigenvectors of matrices," Physical Review E, vol. 74, 036104, 2006.

[9] T. M. Cover & J. A. Thomas, Elements of Information Theory, 2nd ed. Hoboken, NJ: Wiley, 2006.

[10] P. Fiedor, "Networks in financial markets based on the mutual information rate," Physical Review E, vol. 89, 052801, 2014.

[11] M. Rosvall & C. T. Bergstrom, "Maps of random walks on complex networks reveal community structure," Proceedings of the National Academy of Sciences, vol. 105, no. 4, pp. 1118-1123, 2008.

[12] M.Meila, "Comparingclusterings-aninformationbaseddistance,"JournalofMultivariateAnalysis, vol. 98, no. 5, pp. 873-895, 2007.

[13] S. Fortunato & M. Barthelemy, "Resolution limit in community detection," Proceedings of the National Academy of Sciences, vol. 104, no. 1, pp. 36-41, 2007.

[14] V. D. Blondel, J.-L. Guillaume, R. Lambiotte, & E. Lefebvre, "Fast unfolding of communities in large networks," Journal of Statistical Mechanics: Theory and Experiment, P10008, 2008.

[15] G. A. Darbellay & I. Vajda, "Estimation of the information by an adaptive partitioning of the observation space," IEEE Transactions on Information Theory, vol. 45, no. 4, pp. 1315-1321, 1999.

[16] L. F. Kozachenko & N. N. Leonenko, "Sample estimate of the entropy of a random vector," Problems of Information Transmission, vol. 23, no. 2, pp. 9-16, 1987.

[17] L. Paninski, "Estimation of entropy and mutual information," Neural Computation, vol. 15, no. 6, pp. 1191-1253, 2003.

[18] C. E. Shannon, "A Mathematical Theory of Communication," Bell System Technical Journal, vol. 27, no. 3-4, pp. 379-423 and 623-656, 1948.

[19] G. Bonanno, G. Caldarelli, F. Lillo, & R. N. Mantegna, "Topology of correlation-based minimal spanning trees in real and model markets," Physical Review E, vol. 68, 046130, 2003.

[20] J.-P. Onnela, K. Kaski, & J. Kertész, "Clustering and information in correlation based financial networks," European Physical Journal B, vol. 38, no. 2, pp. 353-362, 2004.

[21] T. Aste, T. Di Matteo, & S. T. Hyde, "Complex networks on hyperbolic surfaces," Physica A: Statistical Mechanics and its Applications, vol. 346, no. 1-2, pp. 20-26, 2005.

[22] M. Tumminello, T. Di Matteo, T. Aste, & R. N. Mantegna, "Correlation based networks of equity returns sampled at different time horizons," European Physical Journal B, vol. 55, no. 2, pp. 209-217, 2007.

[23] T. Di Matteo, F. Pozzi, & T. Aste, "The use of dynamical networks to detect the hierarchical organization of financial market sectors," European Physical Journal B, vol. 73, no. 1, pp. 3-11, 2010.

[24] T. Aste, W. Shaw, & T. Di Matteo, "Correlation structure and dynamics in volatile markets," New Journal of Physics, vol. 12, 085009, 2010.

[25] T. Aste, R. Gramatica, & T. Di Matteo, "Exploring complex networks via topological embedding on surfaces," Physical Review E, vol. 86, 036109, 2012.

[26] F. Musciotto, L. Marotta, S. Miccichè, & R. N. Mantegna, "Bootstrap validation of links of a minimum spanning tree," Physica A: Statistical Mechanics and its Applications, vol. 512, pp. 1032- 1043, 2018.