Density Forecasts of Lean Hog Futures Price

High price variability in agricultural commodities increases the importance of accurate forecasts. Density forecasts estimate the future probability distribution of a random variable, offering a complete description of risk. In this paper we investigate density forecast of lean hog prices for the 2002-2012 period for two weeks horizons. We estimate historical densities using GARCH models with different error distributions and generate forward looking implied distributions, obtaining risk-neutral densities from the information contained in options prices. Real-world densities, which incorporate risk, are obtained by parametric and non parametric calibration of the risk-neutral densities. Then the predictive accuracy of the forecasts is evaluated and compared. Goodness of fit and out of sample log-likelihood comparisons indicate that real-world densities outperform risk-neutral and historical densities, suggesting the presence of risk premiums in the lean hog markets. For the historical density forecasts, GED error distributions for the GARCH estimations show an adequate predictive accuracy. Meanwhile, historical densities with normal and t-distributions show a discrete performance.