With topological data analysis, predicting stock market crashes

Authors

  • Nugroho Agung Prabowo Universitas Muhammadiyah Magelang, Indonesia
  • R Arri Widyanto Universitas Muhammadiyah Magelang, Indonesia
  • Mukhtar Hanafi Universitas Muhammadiyah Magelang, Indonesia
  • Bambang Pujiarto Universitas Muhammadiyah Magelang, Indonesia
  • Meidar Hadi Avizenna Universitas Muhammadiyah Magelang, Indonesia

DOI:

https://doi.org/10.47738/ijiis.v4i1.78

Keywords:

TDA, Market Crashes, Stock Detection, Topology

Abstract

We are investigating the evolution of four big US stock market indexes' regular returns after the 2000 technology crash and the 2007-2009 financial crisis. Our approach is based on topological data processing (TDA). To identify and measure topological phenomena occurring in multidimensional time series, we use persistence homology. We obtain time-dependent point cloud data sets using a sliding window, which we connect a topological space for. Our research indicates that a new method of econometric analysis is offered by TDA, which complements the traditional statistical tests. The tool may be used to predict early warning signs of market declines that are inevitable.

References

H. Edelsbrunner, D. Letscher, and A. Zomorodian, “Topological persistence and simplification,” Discret. Comput. Geom., vol. 28, no. 4, pp. 511–533, 2002, doi: 10.1007/s00454-002-2885-2.

A. Zomorodian and G. Carlsson, “Computing persistent homology,” Proc. Annu. Symp. Comput. Geom., vol. 274, pp. 347–356, 2004, doi: 10.1145/997817.997870.

G. Carlsson, Topology and data, vol. 46, no. 2. 2009.

F. Chazal, H. T. Data, and A. Handbook, “High-Dimensional Topological Data Analysis Frédéric Chazal To cite this version : HAL Id : hal-01316989 HIGH-DIMENSIONAL TOPOLOGICAL DATA ANALYSIS,” 2016.

C. Maria, J. D. Boissonnat, M. Glisse, and M. Yvinec, “The Gudhi library: Simplicial complexes and persistent homology,” Lect. Notes Comput. Sci. (including Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinformatics), vol. 8592 LNCS, pp. 167–174, 2014, doi: 10.1007/978-3-662-44199-2_28.

B. T. Fasy, J. Kim, F. Lecci, and C. Maria, “Introduction to the R package TDA,” no. January 2015, pp. 1–16, 2014, [Online]. Available: http://arxiv.org/abs/1411.1830.

M. Kramar, A. Goullet, L. Kondic, and K. Mischaikow, “Persistence of force networks in compressed granular media,” Phys. Rev. E - Stat. Nonlinear, Soft Matter Phys., vol. 87, no. 4, pp. 1–8, 2013, doi: 10.1103/PhysRevE.87.042207.

T. Nakamura, Y. Hiraoka, A. Hirata, E. G. Escolar, and Y. Nishiura, “Persistent homology and many-body atomic structure for medium-range order in the glass,” Nanotechnology, vol. 26, no. 30, pp. 1–22, 2015, doi: 10.1088/0957-4484/26/30/304001.

P. Skraba, S. Univerity, S. Ca, and L. Guibas, “Persistence-based Segmentation of Deformable Shapes Fr ´,” Work, no. 5, 2006.

K. Turner, S. Mukherjee, and D. M. Boyer, “Persistent homology transform for modeling shapes and surfaces,” Inf. Inference, vol. 3, no. 4, pp. 310–344, 2014, doi: 10.1093/imaiai/iau011.

L. M. Seversky, S. Davis, and M. Berger, “On Time-Series Topological Data Analysis: New Data and Opportunities,” IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit. Work., pp. 1014–1022, 2016, doi: 10.1109/CVPRW.2016.131.

Y. Yao et al., “Topological methods for exploring low-density states in biomolecular folding pathways,” J. Chem. Phys., vol. 130, no. 14, pp. 1–10, 2009, doi: 10.1063/1.3103496.

Y. Lee, S. D. Barthel, P. Dłotko, S. M. Moosavi, K. Hess, and B. Smit, “Quantifying similarity of pore-geometry in nanoporous materials,” Nat. Commun., vol. 8, no. May, 2017, doi: 10.1038/ncomms15396.

V. De Silva and R. Ghrist, “Homological Sensor Networks Sensors and Sense-ability.”

Downloads

Published

2021-03-01

Issue

Vol. 4 No. 1: March 2021

Section

Articles

License

Authors who publish with IJIIS : International Journal on Informatics and Information Systems agree to the following terms: Authors retain copyright and grant the IJIIS : International Journal on Informatics and Information Systems right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY-SA 4.0) that allows others to share (copy and redistribute the material in any medium or format) and adapt (remix, transform, and build upon the material) the work for any purpose, even commercially with an acknowledgement of the work's authorship and initial publication in IJIIS : International Journal on Informatics and Information Systems. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in IJIIS : International Journal on Informatics and Information Systems. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).