During the past years, adaptive video based on HTTP has become very popular. Streaming of the adaptive video relies heavily on an estimation of end-to-end network throughput, which can be challenging especially in mobile networks, where the capacity highly fluctuates. In this work, we propose to predict the network throughput using its past measurements. As the analysis shows, the network throughput forms a long range-dependent process; thus, for the throughput prediction, we apply a fractional ARIMA process and artificial neural networks. Our approach does not require any modifications to the network infrastructure or the TCP stack. The predictions are performed for data traces obtained from measurements of throughput of a real mobile network. As the experiment shows, the obtained traffic models are able to enhance the performance of an adaptive streaming algorithm. Compared to the throughput predictors employed in contemporary systems dedicated to adaptive video streaming, the proposed technique obtains better results when taking into account effectiveness of network capacity utilisation and stability of video play-out.