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This paper demonstrates the use of deep learning and time series data generated from user equipment (UE) beam measurements and positions collected by the base station (BS) to enable handoffs between beams that belong to the same or different BSs. We propose the use of long short-term memory (LSTM) recurrent neural networks with three different approaches and vary the number of lookbacks of the beam measurements to study the performance of the prediction used for the proactive beam handoff. Simulations show that while UE positions can improve the prediction performance, it is only up to a certain point. At a sufficiently large number of lookbacks, the UE positions become irrelevant to the prediction accuracy since the LSTMs are able to learn the optimal beam based on implicitly defined positions from the time-defined trajectories.