A social interaction (so-called higher-order event/interaction) can be regarded as the activation of the hyperlink among the corresponding individuals. Social interactions can be, thus, represented as higher-order temporal networks, that record the higher-order events occurring at each time step over time. The prediction of higher-order interactions is usually overlooked in traditional temporal network prediction methods, where a higher-order interaction is regarded as a set of pairwise interactions. We propose a memory-based model that predicts the higher-order temporal network (or events) one step ahead, based on the network observed in the past and a baseline utilizing pair-wise temporal network prediction method. In eight real-world networks, we find that our model consistently outperforms the baseline. Importantly, our model reveals how past interactions of the target hyperlink and different types of hyperlinks that overlap with the target hyperlinks contribute to the prediction of the activation of the target link in the future.