Connected and Automated Vehicles (CAVs) are likely to have a large impact on the traffic in the near future. Assuming we are able to communicate some commands directly to them, it is of interest to know how CAVs can be used for traffic control. In order to achieve this, we need to understand how such controls affect the rest of the traffic. In this work, we study the influence of a CAV acting as a moving bottleneck, using the CAV's speed as a control input. We discuss the interpretation of the microscopic traffic data in the macroscopic framework, and propose nonparametric methods for learning the micro-macro model describing the interaction between the CAV and the surrounding traffic. We use only the local traffic data in the vicinity of the CAV, and design simple, targeted data collection experiments. This learned model is then used to predict the evolution of the traffic, and the predictions are compared with corresponding data from microscopic simulations.