We expose the dynamics of road fuel demand by employing maximum entropy resampling based interval estimates in a fixed width rolling window framework. Our approach facilitates using a uniform specification in a sequential procedure while also providing robust and efficient estimates that can evolve over time. Ours is also the first study to develop a method for estimating illegal fuel activity. To demonstrate our methodology, we use monthly data between 2003-2012 and focus on the demand for diesel and gasoline in Turkey. The results show estimated monthly illegal activity ranging between 5-23 million liters over the last six years. (C) 2015 Elsevier B.V. All rights reserved.