Statistical Financial Model And Volatility Duration Financial Series

With the information communication becoming more and more closely, the spread and storage of financial data has become more convenient, but it is accompanied by a large number of unexplained financial phenomena. Many interdisciplinary disciplines have emerged in order to explain these financial phenomena, which there is the inter-disciplinary science of finance and physics called "Econophysics". In Econophysics,researchers regard financial markets as a complex dynamical system, treating financial data as physical experiment data, and using various concepts, methods and theories in physics to study the macroscopic law of financial markets which is emerged through self-organization. Using statistical physics model to explain and construct the financial market volatility behavior is a research method of Econophysics. In this paper, we intro-duce the basic and relative knowledge on nearest contact stochastic interacting system which is one of statistical physics models, and on the basis of it, we construct a statis-tical financial model with financial theories. Furthermore, we make the nearest contact stochastic interacting system expand to the finite-range multitype contact stochastic in-teracting system, and it will also be given the corresponding statistical financial model.In order to illustrate the rationality of these models, we compare the daily historical market return series with the return series from the agent-based models by studying their statistical characteristics, which is from two aspects: on the one hand, we focus on the application in financial statistics by the finite-range multitype contact stochastic interacting system which is a new model, therefore we need different methods of statis-tical analysis to improve and verify it; on the other hand, we introduce a new statistic to measure the duration of volatility, and on the basis of the original return series form the above models, we apply the volatility duration financial series from this statistic to study various statistical analysis. These studies can verify our models and statistics are reasonable and meaningful, which can provide a viable solution for the financial market research. This thesis includes the following six parts:In Chapter 1, a brief introduction of backgrounds and the research results at home and abroad has been given, and the main research content of this thesis is also presented.In Chapter 2, two kinds of statistical physical models are introduced, which are the nearest contact stochastic interacting system and the finite-range multitype contact stochastic interacting system. For each statistical physical model, the theoretical basis and how to construct the corresponding statistical financial model are introduced in detail. There are two statistical financial models, which are called the contact stochastic interacting financial model and the finite-range multitype contact stochastic interacting financial model.In Chapter 3, we focus on the statistical analysis of the contact stochastic interact-ing financial model, and introduce a new statistic to measure the duration of volatility.That is, there is a new type of financial time series through converting the simulated return series from the financial model into corresponding volatility duration time series.Then we apply the Zipf analysis and cross-correlation analysis to study the Zipf be-haviors and cross-correlation behaviors of volatility duration time series, respectively.Meanwhile the volatility duration time series from the real data in financial market are also considered for comparative analysis.In Chapter 4, we focus on the statistical analysis of the finite-range multitype con-tact stochastic interacting financial model. For it is a new financial model, firstly, we study the basic statistical behaviors of simulated return series from this model, includ-ing descriptive statistical analysis, normality test and probability density distribution.Then we apply the power-law distribution analysis, autocorrelation analysis, multiscale entropy (MSE) analysis and composite multiscale cross-sample entropy (CMSCE) anal-ysis to study the distribution law, volatility clustering, complexity and asynchrony of simulated return series, respectively. Meanwhile we take the return series from the real data in financial market into account for comparative analysis in order to verify the rationality and feasibility of the new model.In Chapter 5, we focus on the statistical analysis of the volatility duration series from the finite-range multitype contact stochastic interacting financial model. We apply the autocorrelation analysis, Lempel-Ziv complexity (LZC) analysis and multifractal detrended fluctuation analysis (MFDFA) to study the volatility clustering, complexity and multifractal behaviors of volatility duration time series, respectively. the volatility duration time series from the real data in financial market are also considered as well for comparative analysis.In Chapter 6, summarize the innovations and conclusions of this thesis.