Wavelet Energy Entropy for Predictability and Cross-Market Similarity in Crude Oil Benchmarks

We study the predictability and cross-market structural similarity of Brent, WTI, and Dubai crude oil futures by means of a wavelet-based Sharma–Mittal energy entropy measure. The proposed framework combines multiresolution wavelet decomposition with a parametric generalised entropy, allowing the characterisation of informational complexity across scales and entropic parameters. We show that predictability is jointly scale- and parameter-dependent. Despite this dependence, the resulting wavelet entropy surfaces exhibit a high degree of geometric similarity across the three benchmarks. A discrepancy analysis further indicates that cross-market differences are localised in restricted regions of the parameter space, whereas intermediate scales are associated with maximal entropy values. Outside such regions, the entropy surfaces converge. Overall, the results provide evidence of a common multi-scale entropic structure underlying crude oil benchmarks, with regional effects affecting predictability without altering the global structural properties. These findings are consistent with the hypothesis of strong informational integration in global oil markets.