Lyapunov Exponents as Indicators of the Stock Market Crashes

- Soloviev, V.N., Bielinskyi, Andrii, Serdyuk, Oleksandr, Solovieva, Viktoria and Semerikov, Serhiy O. (2020) Lyapunov Exponents as Indicators of the Stock Market Crashes Proceedings of the 16th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer. Volume II: Workshops Kharkiv, Ukraine, October 06-10, 2020 (2732). pp. 455-470. ISSN 1613-0073

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Abstract

The frequent financial critical states that occur in our world, during many centuries have attracted scientists from different areas. The impact of similar fluctuations continues to have a huge impact on the world economy, causing instability in it concerning normal and natural disturbances [1]. The anticipation, prediction, and identification of such phenomena remain a huge challenge. To be able to prevent such critical events, we focus our research on the chaotic properties of the stock market indices. During the discussion of the recent papers that have been devoted to the chaotic behavior and complexity in the financial system, we find that the Largest Lyapunov exponent and the spectrum of Lyapunov exponents can be evaluated to determine whether the system is completely deterministic, or chaotic. Accordingly, we give a theoretical background on the method for Lyapunov exponents estimation, specifically, we followed the methods proposed by J. P. Eckmann and Sano-Sawada to compute the spectrum of Lyapunov exponents. With Rosenstein’s algorithm, we compute only the Largest (Maximal) Lyapunov exponents from an experimental time series, and we consider one of the measures from recurrence quantification analysis that in a similar way as the Largest Lyapunov exponent detects highly non-monotonic behavior. Along with the theoretical material, we present the empirical results which evidence that chaos theory and theory of complexity have a powerful toolkit for construction of indicators-precursors of crisis events in financial markets.

Item Type:	Article
Keywords:	Complex dynamic systems, unstable, chaotic, recurrence plot, Lyapunov exponents, stock market crash, indicator of the crash
Subjects:	Science and knowledge. Organization. Computer science. Information. Documentation. Librarianship. Institutions. Publications > 00 Prolegomena. Fundamentals of knowledge and culture. Propaedeutics > 004 Computer science and technology. Computing. Data processing > 004.9 ІКТ ( Application-oriented computer-based techniques ) > 004.94 Simulation Science and knowledge. Organization. Computer science. Information. Documentation. Librarianship. Institutions. Publications > 3 Social Sciences > 33 Economics. Economic science
Divisions:	Institute for Digitalisation of Education > Department of the Cloud-Вased Systems of ICT in Education
Depositing User:	Сергій Олексійович Семеріков
Date Deposited:	08 Oct 2021 19:13
Last Modified:	08 Oct 2021 19:13
URI:	https://lib.iitta.gov.ua/id/eprint/726865

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