In this paper, we propose a non-linear approach to explain the forward discount anomaly. We use two classes of non-linear models: models with changes in mean and long memory process. Our empirical results show that the non-stationarity of the forward discount series is the causes of the rejection of the Forward Unbiased Hypothesis (FRUH). By investigating the forward discount series, we show that are characterized by a stationary long memory behavior which is amplified by the presence of breaks.