Based On The Stock Index And The Volume Of The Copula Function Correlation Analysis

Copula function, also called connection function, is a new tool of statistics to research dependence relationship between random variables. It can describe non-linear dependence relationship between random variables.This thesis mainly introduce Copula function theory, including its notion, character, classify of Copula function, as well as the expression and description of order dependence coefficient and tail dependence coefficient, method of data simulation, method of parameter estimation and method of testing degree of fitting and arrange them by the numbers.Through combining bypast demonstration research of Copula theory, this article constructs three models what are Gaussian Copula with marginal distribution of Student-t distribution, T-Copula with marginal distribution of GARCH distribution and Archimedean Copulas to study the dependence relationship between index of SZ and its volume, and obtain the tail dependence relationship between index of SZ and its volume through calculating. From the result, it sees Gaussian Copula can catch the dependence relationship between index of SZ and its volume, and work well.Though it is constrained by the estimation method of MLE as using small sample size, its result accords with fact, so it can be as reference; GARCH-Copula model can play well with measuring the fluctuating cluster, but GARCH's parameter estimation and T-Copula function's parameter estimation both rely on sample size, as well as the smooth step's result is not good, leading to the parameter estimation of GARCH marginal distribution is not good, so GARCH-T-Copula did not catch the dependence relationship between index of SZ and its volume; The result of Archimedean Copula model displays the same as the series scatter plot, so it proves method of non-parameter estimation suits for small sample size. Archimedean Copula can describe upper and lower tail dependence of non-symmetry, but its parameter's meaning is not clear. Archimedean Copula model's result shows: index and volume's relationship exist, and tail dependence relationship is significant; Index and volume's tail dependence coefficient is higher than non-tail dependence coefficient, so the dependence coefficient between index and volume will grow when stock price rises or goes down suddenly and sharply; Upper tail and lower tail is not symmetrical, and lower tail is higher than upper tail, so the dependence relationship between index and volume is higher when price goes down sharply than when it rises; From investor's behavior, we can have a interesting conclusion: the probability of investors are unwilling to sell their stock when equity market shrink sharply, leading to volume go down with index is bigger than the probability of investors buy stock as stock price rises sharply, leading to volume rise sharply with index.