Public studies on the dynamics of food staples as important as cereals (grains) are relatively scarce. Here we undertake a preliminary analysis of the time series for corn, wheat, soybean, and oat prices first via classical ARIMA/GARCH models, and later complementing with the more complex Stochastic Volatility (SV) models. The goal is to improve upon the classical results by implementing a Bayesian analysis through the construction of a suitable Markov Chain Monte Carlo Model with improved volatility analysis and forecasting capabilities. The performance of the SV model is benchmarked against the classical ARMA/GARCH approach, and both are discussed as monitoring tools for the volatility prices.