In this work, we consider the problem of “information cascades” – i.e., the virality of social network content on social media – and the specific problem of predicting future cascade size over arbitrary time horizons, given information about the content’s initial popularity growth. These predictions are useful for a number of applications, including early detection of potentially harmful viral content in online social networks. With application to a large collection of content on Facebook over a two-month period, we predict cascades size using an approach based on Hawkes point process models. We present characterizations of various properties of Hawkes point processes, allowing us to identify important temporal features for the underlying prediction tasks; and we discuss scalability of our approach relative to alternatives in the literature. We find that content view event rates exhibit complex temporal patterns and follow an exponentially decaying trend over time horizons spanning several days. Analysis of the accuracy of our proposed prediction models shows that they can achieve a high performance over a wide range of horizons.