The Distribution of Commodity Futures Prices and Risk Estimates

This article compares ARMA-GARCH models under alternative statistical distributions to identify the best fit for risk assessment in selected U.S. agricultural commodity markets. The Kupiec proportion-of-failures test assesses whether actual losses exceed expected losses from each model for rice, soybeans, wheat, corn, cotton, orange juice and live cattle in daily futures prices from 1994 to 2026. In sample, ARMA-eGARCH models with skewed Student-t innovations have the lowest AIC and give correct 5% Value-at-Risk coverage for all seven commodities, whereas models with normal innovations are rejected for five of the seven. Out of sample (March 2020 to June 2026), the selected models pass the Kupiec test in 26 of 28 cases, while a normal GARCH(1,1) produces too many violations at the 1% level. A GARCH(1,1) with skewed Student-t innovations forecasts Value-at-Risk about as well as the selected models, so the distributional assumption, rather than the complexity of the volatility equation, accounts for most of the gain in accuracy. The study finds, similarly to other studies, that the skewed Student-t distribution works best in fitting kurtosis and skewness for risk analysis purposes.