Cross-correlations between West Texas Intermediate crude oil and the stock markets of the BRIC

In this paper, we investigate the cross-correlation properties between West Texas Intermediate crude oil and the stock markets of the BRIC. We use not only the qualitative analysis of the cross-correlation test, but also take the quantitative analysis of the MF-DXA, confirming the cross-correlation relationship between West Texas Intermediate crude oil and the stock markets of the BRIC (Brazil, Russia, India and China) respectively, which have strongly multifractal features, and the cross-correlations are more strongly multifractal in the short term than in the long term. Furthermore, based on the multifractal spectrum, we also find the multifractality strength between the crude oil WTI and Chinese stock market is stronger than the multifractality strength of other pairs. Based on the Iraq war (Mar 20, 2003) and the Financial crisis in 2008, we divide sample period into four segments to research the degree of the multifractal (ΔH$\Delta H$) and the market efficiency (and the risk). Finally, we employ the technique of the rolling window to calculate the time-varying EI  (efficiency index) and dependent on the EI  , we can easily observe the change of stock markets. Furthermore, we explore the relationship between bivariate cross-correlation exponents (_Hxy(q)$H_{xy}\left(q\right)$) and the generalized Hurst exponents.