This thesis evaluates two models for time series forecasting in terms of uncertainty. The one is traditional ARIMA model evaluate its parameters by Maximum Likelihood Evaluation (MLE) and uses confidence intervals to denote the uncertainty and another is Bayesian ARIMA model uses credible intervals of posterior distribution to denote uncertainty. The dataset is simulated with fixed arguments which set AR and MA to be 1, 3, 5 respectively. The result shows that the uncertainty of forecasting from the Bayesian model is higher than from traditional ARIMA model evaluated by Mean Interval Score. The accuracy of the prediction in Bayesian ARIMA model has less error than in traditional ARIMA model in most of the data evaluated by Mean Square Error.