Event detection is one of the most important areas of complex network research. It aims to identify abnormal points in time corresponding to social events. Traditional methods of event detection, based on first-order network models, are poor at describing the multivariate sequential interactions of components in complex systems and at accurately identifying anomalies in temporal social networks. In this article, we propose two valid approaches, based on a higher-order network model, namely, the recovery higher-order network algorithm and the innovation higher-order network algorithm, to help with event detection in temporal social networks. Given binary sequential data, we take advantage of chronological order to recover the multivariate sequential data first. Meanwhile, we develop new multivariate sequential data using logical sequence. Through the efficient modeling of multivariate sequential data using a higher-order network model, some common multivariate interaction patterns are obtained, which are used to determine the anomaly degree of a social event. Experiments in temporal social networks demonstrate the significant performance of our methods finally. We believe that our methods could provide a new perspective on the interplay between event detection and the application of higher-order network models to temporal networks.