Long Memory, Multifractality and Forecasting in Strategic Commodity Futures for Colombia: Evidence from Coffee, Oil and Gold Markets

This study analyzes long memory, multifractality and forecasting performance in coffee, Brent oil and gold futures, three international commodity markets of strategic relevance for Colombia. Daily future prices from 2016 to 2025 were examined using logarithmic returns, descriptive statistics, rolling volatility, Hurst R/S, detrended fluctuation analysis (DFA), multifractal detrended fluctuation analysis (MF-DFA), out-of-sample forecasting models, conditional-volatility models and Monte Carlo simulation. The results show heterogeneous long-memory evidence across commodities and market regimes. R/S estimates suggested persistence in the three markets, while DFA moderated this conclusion. MF-DFA confirmed multifractal behavior in all series, with gold and Brent showing wider heterogeneity than coffee. Forecasting results showed that simple models, particularly Random Walk and drift specifications, were difficult to outperform in one-step-ahead predictions. Monte Carlo simulations generated probabilistic price scenarios for 30-, 60- and 90-trading-day horizons, and an ex-post validation with 2026 observed prices showed that six of nine realized prices fell within the simulated P5-P95 intervals. Overall, the findings suggest that commodity futures relevant to Colombia exhibit differentiated forms of temporal complexity, risk and scenario uncertainty that cannot be fully captured by linear models or average volatility measures.