Laplacian spectra of persistent structures in Taiwan, Singapore, and US stock markets
An important challenge in the study of complex systems is to identify appropriate effective variables at different times. In this paper, we explain why structures that are persistent with respect to changes in length and time scales are proper effective variables, and illustrate how persistent struc...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/171077 |
| _version_ | 1811678711896866816 |
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| author | Yen, Peter Tsung-Wen Xia, Kelin Cheong, Siew Ann |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Yen, Peter Tsung-Wen Xia, Kelin Cheong, Siew Ann |
| author_sort | Yen, Peter Tsung-Wen |
| collection | NTU |
| description | An important challenge in the study of complex systems is to identify appropriate effective variables at different times. In this paper, we explain why structures that are persistent with respect to changes in length and time scales are proper effective variables, and illustrate how persistent structures can be identified from the spectra and Fiedler vector of the graph Laplacian at different stages of the topological data analysis (TDA) filtration process for twelve toy models. We then investigated four market crashes, three of which were related to the COVID-19 pandemic. In all four crashes, a persistent gap opens up in the Laplacian spectra when we go from a normal phase to a crash phase. In the crash phase, the persistent structure associated with the gap remains distinguishable up to a characteristic length scale ϵ* where the first non-zero Laplacian eigenvalue changes most rapidly. Before ϵ*, the distribution of components in the Fiedler vector is predominantly bi-modal, and this distribution becomes uni-modal after ϵ*. Our findings hint at the possibility of understanding market crashs in terms of both continuous and discontinuous changes. Beyond the graph Laplacian, we can also employ Hodge Laplacians of higher order for future research. |
| first_indexed | 2024-10-01T02:57:37Z |
| format | Journal Article |
| id | ntu-10356/171077 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:57:37Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | ntu-10356/1710772024-08-07T02:44:08Z Laplacian spectra of persistent structures in Taiwan, Singapore, and US stock markets Yen, Peter Tsung-Wen Xia, Kelin Cheong, Siew Ann School of Physical and Mathematical Sciences Graph Laplacian Stock Market An important challenge in the study of complex systems is to identify appropriate effective variables at different times. In this paper, we explain why structures that are persistent with respect to changes in length and time scales are proper effective variables, and illustrate how persistent structures can be identified from the spectra and Fiedler vector of the graph Laplacian at different stages of the topological data analysis (TDA) filtration process for twelve toy models. We then investigated four market crashes, three of which were related to the COVID-19 pandemic. In all four crashes, a persistent gap opens up in the Laplacian spectra when we go from a normal phase to a crash phase. In the crash phase, the persistent structure associated with the gap remains distinguishable up to a characteristic length scale ϵ* where the first non-zero Laplacian eigenvalue changes most rapidly. Before ϵ*, the distribution of components in the Fiedler vector is predominantly bi-modal, and this distribution becomes uni-modal after ϵ*. Our findings hint at the possibility of understanding market crashs in terms of both continuous and discontinuous changes. Beyond the graph Laplacian, we can also employ Hodge Laplacians of higher order for future research. Published version 2023-10-11T06:49:30Z 2023-10-11T06:49:30Z 2023 Journal Article Yen, P. T., Xia, K. & Cheong, S. A. (2023). Laplacian spectra of persistent structures in Taiwan, Singapore, and US stock markets. Entropy, 25(6), 846-. https://dx.doi.org/10.3390/e25060846 1099-4300 https://hdl.handle.net/10356/171077 10.3390/e25060846 37372190 2-s2.0-85163872159 6 25 846 en Entropy 10.21979/N9/UCEELS © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). application/pdf |
| spellingShingle | Graph Laplacian Stock Market Yen, Peter Tsung-Wen Xia, Kelin Cheong, Siew Ann Laplacian spectra of persistent structures in Taiwan, Singapore, and US stock markets |
| title | Laplacian spectra of persistent structures in Taiwan, Singapore, and US stock markets |
| title_full | Laplacian spectra of persistent structures in Taiwan, Singapore, and US stock markets |
| title_fullStr | Laplacian spectra of persistent structures in Taiwan, Singapore, and US stock markets |
| title_full_unstemmed | Laplacian spectra of persistent structures in Taiwan, Singapore, and US stock markets |
| title_short | Laplacian spectra of persistent structures in Taiwan, Singapore, and US stock markets |
| title_sort | laplacian spectra of persistent structures in taiwan singapore and us stock markets |
| topic | Graph Laplacian Stock Market |
| url | https://hdl.handle.net/10356/171077 |
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