Unveiling heterogeneities of relations between the entire oil–stock interaction and its components across time scales

The oil–stock interaction characterized by complexity and nonlinearity makes relevant research difficult; this is caused by the intricate components of the entire market from a variety of time horizons. However, the heterogeneous influence of the multiscale market components on the entire oil–stock interaction has still been covered. Our objective is to further explore that which time scale is more essential to the integrated market interaction and the dynamic evolution of decisive time scale over time. The Brent spot oil price and the Morgan Stanley Capital International world stock index on a daily frequency were selected as the sample data, and the wavelet transform, the gray correlation, and network analyses were applied succinctly to conduct holistic and dynamical analyses. The primary findings are as follows: The wavelet-decomposed results indicate that impacts of oil price shocks on the oil–stock nexus differ in the long- and short-terms. From the holistic aspect, the growing wavelet variance with time scales demonstrates that long-term changes could lead to structure changes in trend of original market interactions. The wavelet correlation proves that short-term components are dominant in the original interaction and capture the dynamic information effectively. There are no significant lead–lag relations between the original oil–stock interaction and its components. From the dynamic perspective, it is confirmed that components from both the long and short terms are determined. The low and high transmission ability could be helpful to discover the structure changes caused by long-term components and modes controlling more information associated with the short-term components, respectively. The clustering effect limits major modes into a small amount.