Stochastic Interactive Financial Model And Statistical Analysis Of Financial Time Series

With the deepening of the research on modern financial markets,the financial mar-ket has been newly defined as an open non-linear complex system that interacts with a large number of traders and each responds to external information in order to obtain the optimal price for the transaction.And the research on the fluctuant dynamics of this nonlinear complex system has led to the development of some emerging interdis-ciplinary disciplines such as financial mathematics,financial engineering,and financial physics.Two hot areas of research in this subject are the empirical analysis of econom-ic and financial markets and the construction of a theoretical model that embraces all the essential features of financial markets.This essay will start a new exploration of the above two hot research directions.With the development of financial physics,some classical statistical physics particle models are gradually applied to the research of the evolution mechanism of the simulated financial market,and many outstanding research results have been achieved.The first important innovation of this paper is to construct two new dynamic models of financial price using stochastic interaction disease mod-el and small-world network-based epidemic model respectively-Stochastic Interactive Financial Price Model I and Dynamic Model of Financial Price Based on Small World Network II.By using the transmission mechanism of the virus in the infectious disease model between individuals to simulate the transmission mechanism of the information in the financial market between investors,this paper explores the evolution mechanism of the price fluctuation caused by the information exchange in the financial market from a micro perspective.And by discovering the similar statistical characteristics between the model simulation data and real stock market returns time series,we successfully verify the rationality and validity of the two new dynamic models of financial prices.The second important innovation of this paper is to use the existing statistical methods to analyze the statistical characteristics of the stock market price changes from a new perspective.The three-dimensional view is introduced into the result display,which op-timizes the comparison process of empirical analysis.The third important innovation of this paper is to introduce a new effective statistical method to quantify the complexity of multiple time series in financial markets-multivariate multiscale entropy analysis and get new research results.For example,the complexity of the stock market varies and exhibits a significant downward trend in each trading hour.The stock market's system complexity in the morning is obviously higher than that in the afternoon.The specific research contents are as follows:Chapter 2:Combining with the Black-Scholes option pricing formula,and using the stochastic interaction disease model and the epidemic model based on small world network,we construct two new dynamic models of financial prices-Stochastic Inter-active Financial Price Model I and Dynamic Model of Financial Price Based on Small World Network II.With reference to modern financial theory,the two assumptions of setting model are:1)there is the herd effect in the system;2)the differences in investor rationality will affect the investor's herding effect.Through the quantitative analysis of parameters,the parameter combinations of each model are introduced.In order to pre-liminarily prove the rationality of the model,we carried out experiments on the basic descriptive statistics of the empirical data and the simulated data simultaneously.Chapter 3:Statistical Analysis Based on Stochastic Interactive Financial Price Model I.Based on descriptive statistical analysis,power-law exponent analysis,K-S test,correlation dimension analysis,modified multiscale entropy analysis,composite multiscale entropy analysis,the ensemble empirical mode decomposition and Zipf be-havior analysis,the statistical characteristics of the real stock return time series and the simulation data from the Stochastic Interactive Financial Price Model I are analyzed.In the above analysis results,the similarity of statistical features verifies the rationality and validity of the Stochastic Interactive Financial Price Model I.And we found that the initial distribution of the infected patients,the virus transmission rate,the cut-off time of the model,the ratio of impact factors of the type-inf investors and type-imm investors,are all positively correlated with the complexity of the model system.Chapter 4:Statistical Analysis Based on Dynamic Model of Financial Price Based on Small World Network ?.By using the modified R/S analysis and multifractal de-trended fluctuation analysis,we validate that both the real stock market daily returns series and the the simulation data have positive correlation,volatility resistent and mul-tifractal features,which also verifies the rationality and effectiveness of the Dynamic Model of Financial Price Based on Small World Network II.And we found that the virus transmission rate,the ratio of impact factors of the type-inf investors and type-imm investors,are all positively correlated with the long memory of simulated data.In the process of statistical analysis,by comparing the results of multiple fractal be-tween the random rearrangement sequence and the original time series,we find that the internal correlation of time series will affect its multifractal characteristics.Using the advantages of model data,which can adjust the length of sequence,the finite length effect of multifractal spectrum in multifractal detrended fluctuation analysis is verified.Chapter 5:Introducing multivariate multiscale sample entropy analysis into the complexity analysis of multivariate time series of financial stock returns.We find that the systematic complexity of SSE and SZSE varies from hour to hour,showing a sig-nificant downward trend.The stock market's system complexity in the morning is obvi-ously higher than that in the afternoon.Through the analysis of random rearrangement multivariate series and absolute multiple yield series,it is found that the random shuf-fling of multivariate stock return rate time series increases its complexity,and compared with the original data,the time series of absolute multiple time series tend to exhibit long-range correlation on multiple time scales.Finally,we find that the three return time series in the U.S.stock market are not the most complex.However,The complex-ity of its multivariate time series is the highest,followed by the stock markets in Asia and Europe.