We propose a link prediction method for evolving networks. Our method first computes a number of different node similarity scores (e.g. Common Neighbor, Preferential Attachment, Adamic-Adar, Jaccard) and their weighted versions, for different past time periods. In order to predict the future node similarity scores, a powerful time series forecasting model, ARIMA, based on these past node similarity scores is used. This time series forecasting based approach enables link prediction based on modeling of the change of past node similarities and also external factors. The proposed link prediction method can be used for evolving networks and prediction of new or recurring links. We evaluate the link prediction performances of our proposed method and the previously proposed time series and similarity based link prediction methods under different circumstances by means of different AUC measures. We show that, the link prediction method proposed in this article results in a better performance than the previous methods.