This paper introduces a new econometric model of the mispricing associated with (contemporaneous) differences between spot and futures prices. Like existing models, this model assumes that the level of arbitrage activity is positively related to the magnitude of absolute mispricing. However, unlike existing models, the new model assumes that a parameter governing a key feature of this relationship varies over time. Specifically, several versions of a smooth transition model of mispricing are introduced that each allow the shape of the transition function to be determined by a set of explanatory variables. Using high frequency data from the S&P 500 spot and futures market, the results show that the nature of the non-linearity in mispricing corresponds to arbitrageur behaviour that varies (in a periodic fashion) over the trading day. This is evinced by the superior fit of the new model of mispricing, in comparison to the results based on existing econometric models of mispricing. Finally, the observed periodicity in arbitrageur behaviour indicates that arbitrageurs prefer to trade during certain periods within the trading day – a result that contradicts the findings obtained when using existing econometric models of mispricing.