Structure of cross-correlation between stock and oil markets

We displayed in this paper the structure of cross-correlation between the S&P 500 stock market and the Brent Oil market and its evolutionary behavior. Technically, the ensemble empirical mode decomposition is adopted to separate the two series into components. Let a window slide along the multi-variate series of the components, generating a series of segments. For each segment, one calculates the mutual entropies between the components to describe the coupling strengths, resulting into a network between/within the two markets. The networks corresponding to the successive segments form a temporal network. It is found that the characteristic period of intrinsic mode for each series grows exponentially from several days to more than ten years. The couplings between long-term components (with periods larger than one year) form the stable backbone of the network. The shocks of short-term events on the long-term components determine mainly the evolutionary behavior, especially the changes of the coupling structure. This method can be extended straightforwardly to display the cross-correlation structures and their evolutions for complex systems composed of multi-subsystems. Copyright (C) 2022 EPLA