We explore the robustness, efficiency and accuracy of the multi-scale forecasting in crude oil markets. We adopt a novel hybrid wavelet auto-ARMA model to detect the inherent nonlinear dynamics of crude oil returns with an explicitly defined hierarchical structure. Entropic estimation is employed to calculate the optimal level of the decomposition. The wavelet-based forecasting method accounts for the chaotic behavior of oil series, whilst captures drifts, spikes and other non-stationary effects which common frequency-domain methods miss out completely. These results shed new light upon the predictability of crude oil markets in nonstationary settings. (C) 2019 Elsevier B.V. All rights reserved.