Abstract
<jats:p>Commodity futures markets constitute a complex system. The price time series, as manifestations of their intrinsic dynamics, exhibit pronounced non-stationarity, nonlinearity, and multifractal characteristics. Traditional linear models and single-scale analytical frameworks are fundamentally inadequate for capturing the intrinsic dynamical features of such complex systems. Therefore, this paper employs a comprehensive multiscale non-stationary time series analytical framework, integrating four methodologies—multifractal cross-correlation analysis, multiscale complexity measures, time irreversibility diagnostics, and structural break detection—to investigate the non-stationary and nonlinear dynamical features of commodity futures markets. Multifractal Detrended Cross-Correlation Analysis (MF-DCCA) is used to quantify the scale-dependent cross-correlations among WTI crude oil, the US dollar index, and cross-market soybean prices. The Porat–Friedland (PG) irreversibility index measures time-asymmetry across multiple investment horizons. Multiscale Weighted Permutation Entropy (MSWPE) characterizes the complexity hierarchy along the soybean crushing chain (soybean → meal → oil). Jensen–Shannon (JS) divergence-based segmentation detects structural breaks in the WTI price series. We uncover three intriguing phenomena that reveal the characteristics of commodity futures markets as a complex system. First, the scale dependence of market dynamics is not homogeneous across commodities but is fundamentally shaped by supply adjustment elasticity. Energy commodities exhibit pronounced scale-dependent amplification and directional sign reversal at intermediate horizons, while globally tradable agricultural commodities maintain near-monofractal structures across scales, absorbing external shocks as localized noise. Second, through consistent results obtained across multiple analytical methods, we identify an inherent frequency in the market—a characteristic time scale of approximately 20 days—which emerges as the coupling anchor between physical logistics rhythms and financial pricing, potentially representing the intrinsic frequency at which markets digest shocks and complete directional transitions. Third, the persistence of structural reconstruction following shocks depends on the systemic penetration depth of shocks, with exogenous macroeconomic uncertainty exerting stronger and more lasting effects than market-internal events. In summary, supply elasticity, physical logistics rhythms, and systemic penetration depth together constitute the three fundamental determinants of nonlinear dynamics in commodity futures markets, with significant implications for cross-commodity allocation, multi-horizon risk management, and geopolitical scenario analysis.</jats:p>