Multivariate tests of independence and their application in correlation analysis between financial markets

Abstract

We consider the multivariate independence testing problem between pairs of random vectors for high-dimensional data and develop three high-dimensional nonparametric independence tests based on spatial sign and spatial rank, which have greater power than many existing popular tests, especially for heavy-tailed distributions. Under the elliptically symmetric distributions, which are much more general than the widely studied multivariate normal distributions, we establish asymptotic properties of the proposed tests and demonstrate their power superiority via frequently used numerical experiments. To explore the correlation between different financial markets, we first apply the proposed methods to test the dependence between the return rate data of the stocks from US S&P500 index and China CSI300 index, and then apply them to test the dependence between the return rate data of the stocks from the Shanghai Stock Exchange and the Shenzhen Stock Exchange in China.