https://doi.org/10.1140/epjp/s13360-024-05760-5
Regular Article
Spectral fluctuations in financial systems: an integrated random matrix theory and machine learning perspective
1
Department of Physics, Zhejiang Sci-Tech University, 310018, Hangzhou, People’s Republic of China
2
School of Physics, Nankai University, 300071, Tianjin, People’s Republic of China
3
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093, Warsaw, Poland
4
Department of Physics, University of Tabriz, 51664, Tabriz, Iran
5
Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, 51664, Tabriz, Iran
6
School of Materials Science and Engineering, Zhejiang Sci-Tech University, 310018, Hangzhou, People’s Republic of China
7
Department of Opto-Electronics and Information Engineering, College of Precision Instruments and Opto-Electronics Engineering, Tianjin University, 300072, Tianjin, People’s Republic of China
a jalili@zstu.edu.cn, jalili@nankai.edu.cn
f
aixichen@zstu.edu.cn
Received:
23
August
2024
Accepted:
17
October
2024
Published online:
7
November
2024
This study explores the application of random matrix theory (RMT) and machine learning (ML) in the analysis of financial time-series data and market volatility. RMT is used to quantify the level of chaos in financial data, while ML enhances prediction accuracy. We analyze financial data from Bank of America, Bank of China, and Royal Bank of Canada, focusing on spectral statistics and the nearest-neighbor spacing distribution. Using maximum likelihood estimation, we measure the degree of chaos and predict market volatility across daily, weekly, and monthly scales. Our results show that the spectral characteristics of Bank of America and Bank of China align with a Poisson distribution, while the Royal Bank of Canada exhibits a mix of regularity and chaos. Incorporating unfolded prices into the ML model significantly improves predictive accuracy, with the lowest root-mean-square error observed in the Bank of China dataset. Finally, the Cramer–Rao lower bound is applied to minimize estimator variance, confirming the effectiveness of our combined RMT and ML approach. This method bridges statistical physics and advanced data-driven modeling for improved financial predictions.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
