Research On The Evolution Of Nonlinear Dynamics Of Stock Markets Based On Recursive Graphs

The stock market is a real and continuously evolving extremely complex dynamic system,especially the complex system also presents some mutation characteristics.The outbreak of financial crises,such as the "Black Monday" in 1987,the Latin American financial crisis in the 1980 s,the Asian financial crisis in 1997 and the American subprime mortgage crisis in 2008,challenged the classical financial theory based on the linear paradigm.In this context,the research on the complexity of financial system,which is a cross subject of social science and natural science,has gradually emerged and developed.The research on the complexity of financial system mainly focuses on the complexity of financial system.The research paradigm of financial science changes from completely rational,linear and static methods to adaptive,complex and dynamic methods.In this paper,the theory of reconstructed phase space and recursive graph are used to embed one-dimensional stock price time series into high-dimensional phase space,and then the dynamic behavior characteristics of stock market system can be studied by analyzing the recursion of state vector locus in a high-dimensional phase space with topological property equivalent.This paper mainly studies the dynamic evolution behavior of the dynamic characteristics of the stock market,especially the evolution of the dynamic characteristics of the stock market in the process of the formation,deepening and diffusion of the financial crisis from the perspective of complexity science,analyzes the micro mechanism of the financial crisis contagion,deepens the understanding of the contagion process of the financial crisis,and enriches the contagion problem of the financial crisis The theoretical and empirical methods also provide reference for the innovation and transformation of financial research paradigm.The main research contents and conclusions are as follows:(?)This paper analyzes the change of stock market efficiency from the perspective of dynamic evolution.The recursive graph method is used to obtain the dynamic characteristics of stock price time series.The distribution function of diagonal length in recursive graph constructs recursive entropy,which can measure the aggregation degree of state vector embedded in one-dimensional time series into high-dimensional phase space,and the degree of certainty or predictability of the system,and can be used to quantify the effectiveness degree of the stock market.This paper studies the effectiveness of stock market in 14 developed countries(regions)and 12 emerging countries(regions).The results show that the effectiveness of stock market presents a complex cyclical dynamic evolution feature and time scale effect of "relatively effective relatively ineffective relatively effective";the instability of social environment and economic crisis have negative effects on the effectiveness of market;further,empirical mode decomposition method,maximum entropy spectrum analysis method and Fisher method are used It is found that the validity of American stock market has three to five years,11 years and 25 years cycles at different frequencies,which are basically consistent with the three to four years cycle proposed by kichin,about 10 years cycle proposed by Jugra and 15 to 25 years cycle proposed by kunets.(?)The sharp rise and fall of stock price is more and more frequent,especially the stock market crash brings great challenges to the stability of the financial market.In this paper,the recursive graph method and the heuristic segmentation algorithm of nonlinear time series mutation detection are used to detect the time point of market dynamic characteristics mutation before the stock market crash.By analyzing the financial market crashes in 12 developed countries(regions)and 10 emerging countries(regions),it is found that:(1)before the crash of stock market,the market laminar characteristic value Lam will significantly decrease;(2)by recursion analysis of the lam series of American stock market during the financial crisis,it is found that Lam series show fractal like self The similarity structure and the existence of blank bands in the recursive graph show that Lam sequence has phase transition before the stock market crash;(3)using the heuristic segmentation algorithm of nonlinear time series mutation detection,we find that before the market crash,the dynamic characteristics of the market will appear abnormal mutation continuously,and the abnormal mutation time point is 2 to 8 months earlier than the market crash.(?)The nonlinear time series analysis method based on recursive graph method has been paid more and more attention by researchers in various fields,and has been successfully applied to many fields.However,the traditional recursive graph uses the Heavyside step function to judge the recursive behavior of state points in the phase space.There are two problems:(1)the Heavyside step function will produce the rigid boundary problem,resulting in the loss of information;(2)the selection of the critical distance ? is very important.If the selection is not appropriate,the result of recursive analysis will be inaccurate.At present,there is no uniform selection of this parameter Method.In order to solve the above problems,the innovations of this paper are:(1)Gauss function is used instead of Heavyside function to judge the recursion of state phase points,so as to solve the problem of rigidity and binary value of recursion analysis results caused by Heaviside step function;(2)local binary model(LBP)and texture similarity measure earth mover's are used The distance model(EMD)puts forward a new idea of texture analysis on recursive graph for dynamic feature analysis of complex system,and on this basis,constructs a method system to measure dynamic feature similarity of complex system.(?)The adaptive market hypothesis(AMH)holds that financial markets are dynamically evolving,and the market bubble and crash state show complex dynamic changes.AMH hypothesis regards financial market as a complex adaptive system.Under different external background,market characteristics show dynamic evolution.At present,a difficult problem in the study of adaptive market hypothesis is how to quantify the evolutionary behavior of market.In this paper,we construct a method to measure the similarity of dynamic characteristics of complex systems,and make an empirical study on the adaptive market hypothesis from the perspective of the evolution of dynamic characteristics of the stock market.The stock markets of 14 developed countries(regions)and 11 emerging market countries(regions)are studied.The results are as follows:(1)the dynamic characteristics of stock market show dynamic evolution and the evolution behavior of each market has "heterogeneity";(2)the EMD distance of most markets shows a gradual downward trend and the market shows adaptive evolution;(3)annuity in 2008 In the four years before and after the financial crisis,the dynamic characteristics of financial markets in nine emerging countries(regions)have changed dramatically;(4)when China's Shanghai and Shenzhen A-share markets have issued policies with great influence or the market environment has changed significantly,the market dynamic characteristics will have very obvious abnormal changes,such as during the financial crisis in 2008 and the "stock disaster" in 2015,the market dynamic characteristics are shown There is abnormal mutation.(?)Financial crisis contagion has gradually become a focus and difficult problem in the financial field.At present,most of the researches on this problem follow the linear research paradigm and fail to analyze the complex nonlinear characteristics of financial crisis contagion and the internal micro mechanism of financial crisis contagion.This paper attempts to study the contagion of financial crisis from the perspective of complexity science.The basic idea of the study is to regard the financial markets of various countries as dynamic systems with different dynamic characteristics,to dynamically evolve the dynamic characteristics of each financial market before the financial crisis,during the sub-prime crisis and during the European debt crisis,and to build a complex network of dynamic characteristics linkage between financial markets Research.Using the idea of symbolic time series analysis,the linkage of the stock market is symbolized,and then coarsely granulated into a linkage mode composed of five symbols.From the transformation relationship between the linkage modes,the dynamic characteristic linkage mode of the stock market is constructed into a weighted complex network,and the internal micro mechanism of financial crisis infection is explored.The conclusions are as follows:(1)the dynamic characteristics of stock market in different countries have obvious abnormal mutations from 2007 to 2008,and the dynamic characteristics of stock market in different countries have sustained mutations from 2009 to 2011.Compared with the subprime crisis,the global financial market has become more vulnerable during the European debt crisis;(2)the contagion of financial crisis in the global stock market shows a typical“ During the crisis,the complex network structure and the important node composition of the global stock market dynamic characteristic linkage model changed significantly.(?)Because the market environment,investor sentiment and the decision-making of financial institutions are constantly changing,the topological structure of the stock market system network is often in dynamic evolution.The static complex network can provide us with limited information about the complex network of the stock market system,which is easy to "induce" us to have wrong cognition about the complex network of the stock market system.From the perspective of dynamic evolution,this paper uses the method of sliding time window to construct a dynamic evolution network among the dynamic characteristics of 73 stock markets in the world.The conclusions are as follows:(1)the complex network of stock market dynamics shows the typical characteristics of small world network,which shows that the stock market network has a strong ability of information transmission,which explains why the financial crisis in some countries or regions can rapidly expand to other countries or regions.(2)With the deepening of the financial crisis,the average degree value and average clustering coefficient of the network have an increasing trend,the diameter and average path length of the network have a downward trend,the small world network characteristics of the complex network of stock market dynamics characteristics will be further strengthened,the complex network of stock market dynamics characteristics will show a stronger synchronization ability,and the spread range of information between stock markets It will expand significantly,improve the efficiency of information transmission on the network,and further enhance the resonance and linkage between markets.