https://doi.org/10.1140/epjs/s11734-024-01441-7
Regular Article
Nonlinear modeling of financial state variables and multiscale numerical analysis
1
School of Mathematics, Xi’an University of Finance and Economics, 710100, Xi’an, People’s Republic of China
2
Xi’an University of Finance and Economics, China (Xi’an) Institute for Silk Road Research, 710100, Xi’an, People’s Republic of China
3
School of Statistics, Xi’an University of Finance and Economics, Shaanxi, 710100, Xi’an, People’s Republic of China
4
Department of Economics, University of California, 95616, Davis, USA
Received:
16
August
2024
Accepted:
5
December
2024
Published online:
29
January
2025
The aim of this study is to explore the nonlinear modeling of financial state variables and multiscale numerical analysis to better understand the complex dynamic behavior of financial markets. Traditional financial theories are limited by their reliance on linear indicators, failing to adequately capture nonlinear risks in the market. This article first employs Agent-Based Models (ABM) and manifold learning. ABM simulates the heterogeneous behaviors and interactions of market participants, revealing the market's nonlinear characteristics; manifold learning is used for dimensionality reduction of high-dimensional data while preserving the intrinsic geometric structure. Additionally, we utilize multiscale analysis methods to reveal short-term fluctuations and long-term trends in the market. Finally, by calculating the weighted mean escape time and the escape time distribution, we quantify nonlinear phenomena in the market, providing new perspectives for understanding market volatility and systemic risk.
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© The Author(s), under exclusive licence to EDP Sciences, 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.