Crude oil prices are influenced by several events that occur randomly, for example, the weather, the available stocks of oil, the economic growth, the variation in the industrial production, political or geopolitical aspects, exchange rate movements, and so on. Oil price volatility brings uncertainties for the world economy. Despite the difficulty in working with oil price time series, a lot of researches have been developing ways to better understand the stochastic process which represents oil prices movements. This work introduces an alternative methodology, with a Bayesian approach, for the construction of forecasting models to study the returns of oil prices. The methodology introduced here takes in consideration the violation of homoskedasticity and the occurrence of abnormal information, or the non-Gaussian distribution, in the construction of the price forecast models. Moreover, this work examines the relationship between crude oil prices and exchange rate through a cointegration test. The data used in this study consists of the daily closing exchange rate of US dollar to Euro, and oil prices of WTI, West Texas Intermediate, and Brent types, from January 2005 to March 2009. The results do not show the acceptance of cointegration hypothesis. With the presented models, it is possible to infer that the exchange rate is important to explain the oil barrel returns