Downside Risk and Agriculture Commodity Futures Returns: A Study Using Self-Organizing Maps

Abstract

This study analyzes downside risk and nonlinear dependence in agricultural commodity futures using a hybrid framework that integrates Self-Organizing Maps (SOMs) with Copula-based dependence modeling. Agricultural returns exhibit asymmetric behavior, making linear correlation inadequate for risk assessment. The SOM identifies distinct market regimes based on return dynamics and volatility structure, while Student-$t$ and Clayton copulas quantify symmetric and lower-tail dependence within each regime. Results show a clear escalation of dependence from tranquil to crisis states, with tail-dependence coefficients rising monotonically across SOM clusters. The Student-$t$ copula captures symmetric co-movements in extreme returns, whereas the Clayton copula highlights strong joint downside risk during high-volatility phases. These patterns confirm that diversification benefits across agricultural commodities weaken substantially under stress. The proposed SOM–Copula hybrid framework provides a regime-sensitive approach to modeling tail interdependence in commodity markets.