Existing research has demonstrated the effectiveness of hybrid models in improving the accuracy of crude oil forecasting compared to single models. However, these works usually focus on point-valued crude oil closing prices which may suffer from information loss. Instead, this paper proposes a novel interval-based framework based on the principle of “divide and conquer”. After deploying variational mode decomposition (VMD) on an original training series to decompose it into low- and high-frequency components, a newly proposed autoregressive conditional interval (ACI) model is applied to predict the interval-valued low-frequency component which is treated as an inseparable random set, while the interval-valued high-frequency component is predicted by interval long short-term memory (iLSTM) networks. Combination of the two parts yields the final interval-valued prediction. A trading strategy for interval-valued data is designed and executed on a daily basis. Compared to benchmark models and competing trading strategies, the proposed framework can generate superior forecasts and deliver enhanced trading performances. The analysis within this study indicates that the framework’s outstanding performance is robust to various forecasting horizons.