In this paper, a new interval optimization method is proposed to manage the uncertainty of stochastic variables to the problem of Residential Energy Management (REM). This new method is called Stochastic Predicted Bands (SPB) and it considers the uncertainty of decision making variables without knowledge of the Probability Density Function (PDF). The modeling of uncertainty is done by bands based on the prediction of stochastic variables. Besides, an auxiliary parameter is defined to provide flexibility to the decision-maker to be optimistic or conservative. Hence, applying the optimistic coefficient to the SPB method results in the enhancement of its performance. This new method is called Modified Stochastic Predicted Bands (MSPB). The simulation results of the test system show the performance of the proposed model in solving energy management problems via SPB method.