The forward premium anomaly refers to the situation where the slope coefficient in a regression of spot returns on the lagged interest rate differential is negative and significantly different to unity. This paper explores some of the asymmetries and non linearities present in the anomaly and the apparent rejection of Uncovered Interest Parity (UIP). The methodology is motivated by some recent economic theory literature on transactions costs, the limits to speculation and hysteresis. The paper estimates Logistic Smooth Transition Dynamic Regression (LSTR) models with the transition variable being the lagged forward premium for a range of currencies. An inner regime with foreign interest rates exceeding US rates is found to be consistent with the anomaly. While a third and outer regime with US interest rates exceeding foreign rates indicates convergence towards UIP. Detailed Monte Carlo experiments support the finding that an LSTR data generating process can indeed induce the forward premium anomaly. While the methodology appears promising in terms of uncovering important non linear and asymmetric behavior in the relationship, it should be noted that parameter estimation uncertainty indicates quite wide confidence intervals on the estimated transition functions. Hence, the accurate prediction of states, or regimes where UIP has a high probability of holding, is quite hard.