Multivariate realized volatility forecasts of agricultural commodity futures

We forecast the multivariate realized volatility of agricultural commodity futures by constructing multivariate heterogeneous autoregressive (MHAR) models with flexible heteroscedastic error structures that allow for non-Gaussian distribution, stochastic volatility, and heteroscedastic and serial dependence. We evaluate the forecast performances of various models based on both statistical and economic criteria. The in-sample and out-of-sample results suggest that the proposed MHAR models allowing for flexible heteroscedastic covariance structures outperform the benchmark MHAR models. In addition, the proposed Bayesian MHAR models allowing for t innovations improve both in-sample and out-of-sample forecast performance of the corresponding MHAR models with Gaussian innovations.