Forecasting of energy commodity prices across macroeconomic periods: a comparative analysis using alternative models

This study aims to assess and compare the predictive performance of advanced forecasting approaches, including stochastic models, like the Geometric Brownian Motion (GBM), Fractional Brownian Motion (FBM), and Brownian Bridge (BB), as well as a Machine Learning (ML) model, the Long Short-Term Memory (LSTM), in predicting the price movements of energy commodities such as Brent oil, crude oil, gas oil, heating oil, and natural gas across eight geopolitical and macroeconomic events. To reassess the role of persistence in energy commodity prices, the study strengthens the Hurst analysis by combining classical rescaled range analysis with detrended fluctuation analysis, the Geweke–Porter–Hudak estimator, Lo’s modified rescaled range statistic, bootstrap confidence intervals, and Generalized Autoregressive Conditional Heteroskedasticity (GARCH)-filtered residual diagnostics. The forecasting results further indicate that no single model dominates uniformly across all commodities and crisis regimes. BB records the most frequent best performance across the main accuracy criteria, while LSTM, GBM, and FBM remain competitive in specific commodity–period combinations. During the most recent period, with the Russia-Ukraine Conflict, GBM, FBM, and BB demonstrated strong forecasting performance across different time horizons, achieving an average Mean Absolute Percentage Error (MAPE) of less than 10% for crude oil and Brent oil and below 20% for heating oil and gas oil, based on 1,000 simulations. These results highlight the comparative effectiveness of both ML and stochastic methods, offering valuable insights and practical tools for policymakers and market agents to manage energy price risks more effectively.