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Stochastic Financial Model And Statistical Analysis On Correlation And Complexity

Posted on:2019-04-21Degree:DoctorType:Dissertation
Country:ChinaCandidate:W ZhangFull Text:PDF
GTID:1319330545972301Subject:Statistics
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The emergence of econophysics provides a new perspective for studying financial issues,financial models reproduce the stylized facts observed in the financial market through simulating the dissemination process of investment information in the financial market with microscopic interaction of particles in statistical physical models.Many traditional methods are ineffective because of nonlinear and nonstationary characteristics of financial time series,and many new methods have come into being.In this paper,three kinds of financial markets stock price evolution models are constructed by the percolation on sierpinski gasket,stochastic exclusion process,and the combination of stochastic exclusion process and compound poisson process.Some statistical anal-ysis methods are improved for the analysis of nonlinear,nonstationary financial time series,and the comparative statistical analysis of the correlation and complexity for the simulation and real return series are implemented.Specifically,the structure of the full thesis is as follows:In the chapter 1,the research background,the main theoretical basis and the main contents of this thesis are introduced.In the chapter 2,the stochastic exclusive financial price model is introduced,where the spread of market investors' trading attitude is imitated by the particles' interaction process.The analyses on correlation and complexity are comparatively implemented with the real ones,to verify the rationality of the financial price model in the statistical sense.Firstly,the leptokurtic,fat-tailed distribution and volatility clustering of the simulation series with different rates for the financial model are discussed.Secondly,timedependent intrinsic detrended cross-correlation is proposed to be based on the detrended cross-correlation and the time-dependent intrinsic correlation,and it is used to analyze the IMF pairs obtained by EEMD of real and simulation return series.Thirdly,the tail distribution is analyzed by power-law,complexity behavior is analyzed by LZC,the complexity of the absolute returns with different power exponent is also studied.Finally,the chaotic behavior of return series is analyzed by correlation dimension and Lyapunov exponent.We find that the simulation return series can show the similar statistical characteristics of returns of the real market index through the comparative study of the simulation data with the real series,which verifies the stochastic exclusive financial price model is reasonable to some extent.In the chapter 3,a nonlinear financial price model is introduced to be based on the percolation on the Sierpinski gasket,where the trading attitude can be spread along the open side of the Sierpinski gasket,a cluster containing the original point representatives a group of investors who share the same trading attitude toward the stock market.The probability p of edge is open in the Sierpinski gasket represents the possibility that adjacent investors interact.A series of statistical analyses are done.Firstly,the power-law behavior of the tail of the simulation return with different p is studied.Secondly,the complexity behavior of the simulation return with different p is studied.Finally,fractional ordinal array complexity is proposed to be based on fractional calculus and ordinal array complexity to explore the fractional order information of financial time series,and it is used to analyze the simulation and real series.The empirical results show that,the financial price model based on the percolation on the Sierpinski gasket can seize the power-law behavior and the complexity dynamics of financial market to some extent,and the model is reasonable and effective.In chapter 4,a novel stochastic statistical physics financial system,which is constructed by the combination of stochastic exclusion process and compound Poisson process,is introduced.The two parts are concerning with stock return fluctuations caused by the dissemination of investors' trading attitudes and random drastic fluctuations caused by the macroeconomic factors,respectively.Firstly,it is verified that the price model is a Levy process.Secondly,the multifractal nature is explored with the multifractal detrended cross-correlation analysis(MF-DCCA).Finally,fractional fuzzy entropy is proposed to be based on fractional calculus and fuzzy entropy,and the empirical analyses of fuzzy entropy and fractional fuzzy entropy on simulation and real return are implemented.The empirical results show that the proposed model with the appropriate parameters can grasp the dynamics of some important financial market complexities to some extent.In chapter 5,the findings of this thesis and a summary of innovations are introduced.
Keywords/Search Tags:exclusion process, time-dependent intrinsic detrended cross-correlation, LZC, Sierpinski Gasket Lattice, fractional fuzzy entropy, fractional ordinal array complexity
PDF Full Text Request
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