Asymmetry Test Of Multivariate Correlation

In the context of different macro-environments,the relationship between financial assets is complicated and asymmetry is widespread.Asymmetry phenomenon for stock assets which performed as the correlation between stock assets will increase in the bear market,and the correlation between stock assets will decrease in the bull market.Considering the financial investment in reality,we have to consider not only stock assets,but also other kinds of financial assets,and the different assets have different asymetric characteristic which may not be consistent with stock assets due to different assets' attributes.For example,in a bear market,the correlation between assets will be decrease,but in the bull market,the correlation between assets will increase.Therefore,this paper draws on Pan Zhiyuan's[1]expression of asymmetry,that is,asymmetry can be described as a phenomenon in which the correlation between assets changes significantly under different macroeconomic conditions[1].In financial markets,if ignored the asymmetric correlation between financial assets may result in lower yields or higher risk costs.Therefore,asymmetric research on the correlation of financial assets is beneficial to allocate the asset portfolio rationally and reduce the risk of financial investment,it has an important significance in the financial markets.This paper proposes an asymmetry test method for the correlation of multiple variables for the correlation between multiple financial assets.This method has the following advantages compared with other asymmetry research methods for the correlation between variables:Firstly,the method proposed in this paper is model-free,not affected by the choice of the model;secondly,the asymmetry test can be performed on the correlation of the multivariate variables,and not only the asymmetry test for binary variables;Finally,the exact judgment result can be given at a given level of significance,with less subjective color.Compared to the asymmetry test statistic for the correlation of binary variables proposed by Hong et al.[2],the test statistic JM proposed in this paper can be performed simultaneously on the correlation of multiple variables.The statistic can be used to test whether this set of variables' asymmetric correlation phenomenon generated by the economic environment changes are obvious,and provide advice on whether to consider the asymmetry of the correlation between the assets and change the investment portfolio of the assets.Based on the above,the test statistic proposed in this paper can obtain the difference between the positive and negative exceedence correlation coefficients among the variables,so the asymmetry test proposed in this paper can not only test the asymmetric correlation of multivariate variables,but also provide a reference for the specific investigation of which two variables have asymmetric correlation.In order to analyze the performance of the statistic JM proposed in this paper,this paper uses the mixing Copula and skew-normal distribution to generate simu-lation data,and analyzes the size and power of the statistic.The results show that the statistic JM proposed in this paper can test the data with different degrees of asymmetry,and the test results are good.In the empirical study,this paper applies different market indexes at home and abroad,including Dow Jones Industrial Av-erage Index,Shanghai Composite Index,SSE Government Bond Index,SSE Fund Index and Hang Seng Index for asymmetry test.The result rejects the null hypoth-esis of the correlation is symmetric,and there is an obvious asymmetric correlation between market indices.