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The Nonlinear Dynamics Research on Extreme Events of Financial Complex System

Author: GuanJie
Tutor: YinKeDong
School: Ocean University of China
Course: Quantitative Economics
Keywords: complexity sciences nonlinear theory extreme events long-range correlations recurrence interval
CLC: F224
Type: Master's thesis
Year: 2013
Downloads: 2
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Abstract


The height and rapid development of the financial markets is one of theimportant characteristics of contemporary economic society. However, when it ismaintaining highly dynamic, it also will lead potential and huge risk losses tous.Therefore, studying the operation of the financial system and understanding theemergence of extreme events is currently one of the important topics in the field offinancial research.The financial market is a very complex dynamics system. It continued to producea large-scale, high-frequency data sequence to record the results of jointdecision-making of many participants in the market (individual) and these records arecomplete and can be continuously recorded. In other words, the financial market is infact a real continuous evolution of complex systems. Moreover, this complex systempresents some kind of emergent nature, I.e., the complex nature of the system is notonly the plus and inferred of the nature of the various components and it mustconsider the interaction and mutual adaptation between the micro-individual.This article is in accordance with the idea of complexity sciences. It closelyintegrates nonlinear system dynamics, through in-depth study of the non-linearcharacteristics of financial time series to examine the law of large fluctuations inextreme events in China’s financial system. First, we analyze the time series of thesecurities market to explore whether it is from independent and identically distributedrandom process. If the data from the non-linear system, we can further use nonlinearquantitative analysis method to calculate the value of nonlinear characteristics. By thevalue of these characteristics, we can determine that the financial system is a chaoticsystem and describe the financial system by the values of these characteristics. If thefinancial system does have a chaotic behavior, we can explore whether the financialtime series is a long-range correlations and extreme events in the financial system isassociated with long-range time. If there is a long-term memory, we can reproduce thetime interval sequence of extreme events in order to reveal the distributioncharacteristics of extreme events in complex financial markets. Finally, we can dosome research in terms of method application and provide relevant recommendationsfor financial risk management. The thesis is divided into five parts:The first part is the basic theoretical research. This section contains a complex scientific theory, the financial complex systems theory and the theory of financialtime series analysis. It describes the theoretical features of financial complex systemand chaos theory in detail. Lay the theoretical foundation for the follow-up to carryout the nonlinear dynamics of complex financial system of extreme events.The second part is deterministic and nonlinear studies of complex financial timeseries. It solves two issues which must be figured out before nonlinear dynamicsresearch namely deterministic and nonlinear inspection of dynamical systems. It alsomakes innovations on test methods and paves the way for later.The third part is the long-range correlations study of extreme events of financialcomplex system. It defines the extreme events of financial complex system accordingto the concept of small and medium-probability event, explores the long-rangecorrelations characteristics of extreme events of financial complex system based onatmospheric physics, which has a major impact on prediction and assessment ofextreme events.The fourth part is the study of recurrence interval based on extreme events offinancial complex system. Financial complex system has long-rangecorrelations.According to the long-term memory, it uses the method of financialphysics recurrence interval to reasoning the recurrence interval distribution of extremeevents, constructs the model of risk assessment taking yield for example and enrichesresearch methods of extreme events of financial complex system.The fifth part is the last chapter and it is the summary and outlook of this paper.This section summarizes the research significance, the specific content of the studyand the conclusions of the paper, points out the contents needing to be improved inthe next step and makes a few suggestions for reference to market regulators.

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