Abstract
This paper aims to discuss the fragilities of hierarchical structures of Chinese financial market, and find out the possible faults. We propose an analysis approach to explore the structure characteristics of financial market based on the manifold structure of financial data. First, we extract the underlying manifold embedded in financial time series data by manifold learning, which governs the dynamics of financial system. Second, the surface curvature of manifold is used to serve the quantitative analysis of manifold structure, in which the rate of curvature change is employed to measure the structure fragility. Finally, the dynamics of manifold structures are discussed by Lyapunov exponents, which further explore the fragilities of markets and confirm the conclusions of curvature analysis. In empirical research, we select CSI 300 index as the overall trend indicator of China's financial market, and nine industry indexes as hierarchical market indicators. Our research results indicate that Chinese financial market has less chaotic than the real economy industries, in spite of its high fragility. Some real economic industries are most likely to crash first in the event of a crisis. The findings contribute to present the states of financial markets and provide decision support for investors.
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References
Ansar, A., Flyvbjerg, B., Budzier, A., & Lunn, D. (2016). Does infrastructure investment lead to economic growth or economic fragility? Evidence from China. Oxford Review of Economic Policy, 32, 360–390.
Baker, M., Wurgler, J., & Yuan, Y. (2012). Global, local, and contagious investor sentiment. Journal of Financial Economics, 104, 272–287.
Beck, T., Tao, C., Chen, L., & Song, F. M. (2016). Financial innovation: The bright and the dark sides. Journal of Banking and Finance, 72, 28–51.
Belkin, M., & Niyogi, P. (2003). Laplacian Eigenmaps for dimensionality reduction and data representation. Neural Computation, 15, 1373–1396.
Benincà, E., Huisman, J., Heerkloss, R., et al. (2008). Chaos in a long-term experiment with a plankton community. Nature, 451, 822–825.
Cao, L. (1997). Practical method for determining the minimum embedding dimension of a scalar time series. Physical D, 110, 43–50.
Casetti, L., Clementi, C., & Pettini, M. (1996). Riemannian theory of Hamiltonian chaos and Lyapunov exponents. Physical Review E, 54, 5969–5984.
Demetrius, L. A. (2013). Boltzmann Darwin and directionality theory. Physics Reports, 530, 1–85.
Dunlop, G. R. (1980). A rapid computational method for improvements to nearest neighbor interpolation. Computers and Mathematics with Applications, 6, 349–353.
Givens, C. R., & Shortt, R. M. (1984). A class of wasserstein metrics for probability distributions. Michigan Mathematical Journal, 31, 231–240.
Haji, A. H., Mahzoon, M., & Emdad, H. (2007). Reconstruction and prediction of the in-cylinder pressure attractor of an internal combustion engine using locally constant models. Nonlinear Dynamics, 48, 437–447.
Han, L. Y., & Christopher, J. R. (2011). Stable Takens’ embeddings for linear dynamical systems. IEEE Transactions on Signal Processing, 59, 4781–4794.
Hui, X. F., & Zhang, A. R. (2020). Construction and empirical research on the dynamic provisioning model of China’s banking sector under the macro-prudential framework. Sustainability, 12(20), 8527.
Jamshidi, A. A., Kirby, M. J., & Broomhead, D. S. (2011). Geometric manifold learning. IEEE Signal Processing Magazine, 28, 69–76.
Kılıç, D. K., & Uğur, Ö. (2018). Multiresolution analysis of S&P500 time series. Annals of Operations Research, 260(1), 197–216.
Kim, K., & Lee, J. (2014). Nonlinear Dynamic Projection for Noise Reduction of Dispersed Manifolds. IEEE Transactions on Pattern Analysis and Machine Intelligence, 36, 2303–2309.
Kinsner, W. (2006). Characterizing chaos through Lyapunov metrics. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, 36, 141–151.
Li, B., Zheng, C. H., & Huang, D. S. (2008). Locally linear discriminate embedding: An efficient method for face recognition. Pattern Recognition, 41, 3813–3821.
Lott, J., & Villani, C. (2009). Ricci curvature for metric-measure spaces via optimal transport. Annals of Mathematics, 169, 903–991.
Lunga, D., Prasad, S., Crawford, M., & Ersoy, O. (2014). Manifold-learning-based feature extraction for classification of hyperspectral data. IEEE Signal Processing Magazine, 31, 55–66.
Menck, P. J., Heitzig, J., Marwan, N., & Kurths, J. (2013). How basin stability complements the linear-stability paradigm. Nature Physics, 9, 89–92.
Ollivier, Y. (2007). Ricci curvature of metric spaces. Computers Rendus Mathematique, 345, 643–6465.
Roweis, S. T., & Saul, L. K. (2000). Nonlinear dimensionality reduction by locally linear embedding. Science, 29, 2323–2326.
Sandhu, R. S., Georgiou, T. T., & Tannenbaum, A. R. (2016). Ricci curvature: An economic indicator for market fragility and systemic risk. Science Advances, 2, e1501495–e1501495.
Sivakumar, B. (2002). A phase-space reconstruction approach to prediction of suspended sediment concentration in rivers. Journal of Hydrology, 258, 149–162.
Sturm, K. T. (2006). On the geometry of metric measure spaces. Acta Mathematica, 196, 65–131.
Sugihara, G., May, R., Ye, H., Hsieh, C., Deyle, E., Fogarty, E. M., & Munch, S. (2012). Detecting causality in complex ecosystems. Science, 338, 496–500.
Takens, F. (1980). Dynamical systems and turbulence. In D. R. Warwick & L. S. Young (Eds.), Detecting strange attractors in turbulence (pp. 366–381). Berlin: Springer.
Talmon, R., Cohen, I., Gannot, S., & Coifman, R. R. (2013). Diffusion maps for signal processing: A deeper look at manifold-learning techniques based on kernels and graphs. IEEE Signal Processing Magazine, 30(4), 75–86.
Tenenbaum, J. B., Sivlar, V. J., & Langford, C. (2000). A global geometric framework for nonlinear dimensionality reduction. Science, 290, 2319–2323.
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We would like to thank reviewers and editors for their comments, which are helpful for us to improve the paper. This research was supported by the Open Research Subject of Key Laboratory (Research Base) of Research Center of FinTech and Entrepreneurial Finance (#JR2017-02), and supported by Sichuan Science and Technology Program (#2019YJ0452).
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Huang, Y., Wan, J. Hierarchical analysis of Chinese financial market based on manifold structure. Ann Oper Res 315, 1135–1150 (2022). https://doi.org/10.1007/s10479-021-03959-8
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DOI: https://doi.org/10.1007/s10479-021-03959-8