Selecting an appropriate Autoregressive Moving Average (ARMA) model for a given time series is a classic problem in statistics that is encountered in many applications. Typically this involves a human-in-the-loop and repeated parameter evaluation of candidate models, which is not ideal for learning at scale. We propose a Long Short Term Memory (LSTM) classification model for automatic ARMA model selection. Our numerical experiments show that the proposed method is fast and provides better accuracy than the traditional Box-Jenkins approach based on autocorrelations and model selection criterion. We demonstrate the application of our approach with a case study on volatility prediction of daily stock prices.