Analysis Of The Dependence Structure Between China's Equity And Commodity Futures Markets Based On Vine Copula Models

The study of dependence structures in financial markets has recently attracted increasing attention among reasearcher and practioners. The trading volume of commodities have grown rapidly in the globe markets since 2000. In recent years, many reaserchers have paid attention to relationship between stock market and commodity futures market. In this paper, we discuss the dependence structure between China's equity market(CSI 300 index) and the three commodity futures index in the Chinese market. The conclusion of this paper can provide empirical evidences to the asset allocation between China's equity market and commodity markets, risk measurement.At the aspect of methodology, the innovations of this paper are listed below: First, we adop the Vine copula method to analyse the dependence structure. Compared with the traditional high dimensional modeling method, vine Copulas overcome many limitations and being flexible for high dimensional modeling. Using two different vine copula structure(canonical vine and d vine), we decompose a 4 dimensional joint distribution into 4 different marginal distribution and several pair copulas, which describe the dependence structure.Second, we adopt SJC copulas(Symmetrized Joe-Clayton) proposed by Patton (2006) as the function to the each pair variables. SJC copula can figure out different dependence structure automatically without any assumptions to each pair. Third, instead of using sequential estimation method (Aas et al.,2009) to eastimate the parameters, we maxmize the likelihood function for global optimization directly, due to the fact that SJC copula can figure out different dependence structure automatically which we don't need visually choose the proper pair copula function one by one.In order to determine the better vine copula structer, we use out of sample VaR method to find out solution from canonical vine and d vine. In the paper, we construct a equally weighted portfolio, which including CSI 300 index and three commodities future(Shanghai copper future index, Dalian soy meal futures index and Shanghai natural rubber index). We backtest 5 different significance level VaR forecastings for 1 week horizon from 2006.10 to 2016.1 using fixed length rolling window. When the condition mean and volatility calculated by the same model, the accuracy of dependence structure can influence the accuracy of VaR forecasting directly. According to the Kupiec test and Christofferson test, we find that the dependence structure estimated by canonical vine provied a btter solution.At last, we analyse the dependence structure between CSI300 index and 3 commodities by cannonical vine copula. Using 3 dependence measurement(linear correlation coefficient, upper tail dependence, lower tail dependence), we conclude 3 features to the dependence structure between CSI300 index and 3 commodities: First, the average correlation between CSI 300 index and commodities is positve but low. Such as the correlation coefficient between Shanghai copper futures index and CSI 300 is 0.241, which the highest value in all pairs. Other results of linear coefficient are 0.142 for Shanghai and Shenzhen 300 index-soybean meal futures and 0.181 for Shanghai and Shenzhen 300 index-natural rubber futures. Second, in the observation period, the dependence between Shanghai and Shenzhen 300 index and all the commodities futures index present the characteristic that lower tail dependence is higher than upper tail dependence which means that the probability that Shanghai and Shenzhen 300 index and commodities futures indexes fall sharply together is higher than they rise markedly together. To be specific, all the commodities futures index present the characteristic that the lower tail dependence is higher than the upper tail dependence except for the natural rubber futures index which does not show obvious asymmetry. Third, though the analyzation of ADF test and the Ljung-Box Q statistic, we find that Shanghai and Shenzhen 300 index and commodities futures indexes all show obvious non-stationary and long memory. So use the DCC model(Engle,2002; Patton,2006) to estimate the time-varing dependence of stock market and commodities futures market may exist deviation.