A bilinear stochastic model is applied, which is initially proposed for analyzing financial returns and other complex systems by combining high non-linearity and multiplicity of noise. Due to its random character, this model does not have a deterministic component which allows considering persistence of stream flows in a hydrology application. Therefore, the combination of a deterministic segment of an order 2 auto-regressive model and the bilinear stochastic model as the random component, and a bilinear auto-regressive model (BAM) is obtained. The BAM was employed to predict stream flows in windows of 3, 6, and 12 months in 12 rivers from several regions of Colombia. The BAM exhibits a simple structure and shows a substantial improvement in error reduction for maximum and minimum flows during the validation period compared to traditional stochastic models.