Forecasting the Conditional Distribution of Interval‐Valued Crude Oil Prices Using a Diffusion‐Based Approach

ABSTRACT The extant literature on forecasting interval‐valued crude oil prices has predominantly focused on estimating the conditional mean, while little attention has been paid to the conditional distribution, which may offer more insightful information. This paper proposes a novel model free interval‐based Treeffuser approach to forecast the conditional distribution of interval‐valued crude oil prices. This approach involves estimating the score function in the inverse stochastic differential equation using gradient boosting trees and generating samples through a diffusion process. Empirical results demonstrate that the proposed approach outperforms classical interval‐based machine learning methods, particularly during extreme events. The superior performance is robust to various forecast horizons and estimation periods. Furthermore, we propose an interval‐based trading strategy that can effectively mitigate volatility and boost returns. Notably, our approach captures the significant impact of extreme events on minimum prices, revealing a dynamic pattern where the range of prices initially widens, and later the distribution of minimum prices flattens out.