The performance of HTTP adaptive streaming (HAS) depends heavily on the prediction of end-to-end network bandwidth. The increasingly popular low latency live streaming (LLLS) faces greater challenges since it requires accurate, short-term bandwidth prediction, compared with VOD streaming which needs long-term bandwidth prediction and has good tolerance against prediction error. Part of the challenges comes from the fact that short-term bandwidth experiences both large abrupt changes and uncertain fluctuations. Additionally, it is hard to obtain valid bandwidth measurement samples in LLLS due to its inter-chunk and intra-chunk sending idleness. In this work, we present DeeProphet, a system for accurate bandwidth prediction in LLLS to improve the performance of HAS. DeeProphet overcomes the above challenges by collecting valid measurement samples using fine-grained TCP state information to identify the packet bursting intervals, and by combining the time series model and learning-based model to predict both large change and uncertain fluctuations. Experiment results show that DeeProphet improves the overall QoE by 17.7%-359.2% compared with state-of-the-art LLLS ABR algorithms, and reduces the median bandwidth prediction error to 2.7%.