Researches And Applications Of Copula Function In Financial Time Series

Correlation analysis is an important issue in financial quantitative analysis,but the financial market is full of randomness,the correlation between financial assets is becoming more and more complex,and the analysis method based on linear correlation coefficient can no longer reflect the relevant information of the financial market comprehensively.Copula function can describe the correlation between variables,especially plays an important role in the correlation analysis of variables with complex structure.It can be used to measure the nonlinear and asymmetric correlation and tail correlation,providing a powerful tool for the research of correlation in the financial field.This paper analyzes the characteristics and properties of Copula function,discusses the financial time series model based on Copula theory,and the Copula function parameter estimation and testing method,studies the application of Copula model in the financial field,and obtains some results.This paper mainly does the following aspects of work:1.The mixed Copula function is composed of linear convex combinations of multiple Copula functions.Compared with the single Copula function,the mixed Copula function has more excellent properties and its application is more flexible.This paper deduces the correlation measure based on the mixed Copula function,obtains the relationship between the correlation measure based on the mixed Copula function and the correlation measure derived from the Copula function in its components,and gives a method to simulate the random variable of the mixed Copula function.2.A method combining maximum likelihood estimation and EM algorithm is proposed to estimate the parameters of the mixed Copula model,and the method is derived in detail,and the feasibility of the algorithm is verified through simulation analysis.The corresponding statistical analysis results are obtained during empirical analysis.3.The Gumbel Copula,Clayton Copula,Frank Copula and mixed Copula model are used to conduct empirical research on the correlation between Shanghai Composite index and Shenzhen component index,and the correlation between Shanghai Composite index and fund index.According to the statistical characteristics of the selected sample data,GARCH model and EGARCH-M-GED model were respectively used to fit the edge distribution.TheCopula model was proposed to be selected intuitively by using the empirical distribution scatter diagram and frequency distribution histogram of sample sequence after transformation of probability integral.The empirical distribution and copulas connect model with variable on the main diagonal u =v the probability distribution of the contrast figure,combining based on Copulas connect function Kendall rank correlation coefficient and Spearman correlation coefficient,Gini coefficient of associated and tail correlation coefficient,found the Mixture Copulas connect model describes the data fat-tailed and correlation characteristics of ability is more outstanding,the effect is better than a single of Copulas connect model.