Conversational partners adapt their speech to one another in a phenomenon called entrainment. While entrainment behaviors are associated with a variety of positive conversational outcomes, they are rarely implemented in dialogue systems due to their poorly understood mechanics. Conversational dynamics models could discover entrainment behavior in a dialogue corpus, but to date they have not been designed for or evaluated in dialogue systems. In this paper, we propose an autoregressive model specifically for use in a dialogue system. We evaluate its ability to predict features for upcoming conversational turns, and show it outperforms several baseline models. Additionally, we analyze its attention mechanism to explain which turns it finds useful for predicting upcoming speech features. Finally, we discuss its potential for future deployment in a live dialogue system.