Pedestrian trajectory prediction can provide decision support for self-driving cars and robots to avoid potential collision risks. Modelling of social relationships and multimodal prediction are core challenges in pedestrian trajectory prediction. However, there are two problems with existing methods: (1) these methods usually focus on modelling pairwise or group interactions, ignoring the importance of high-order interactions; and (2) existing methods struggle to balance the performance between deterministic and multimodal predictions. To address these issues, we propose a higher-order graph attention network for pedestrian trajectory prediction. Specifically, we first construct spatial and temporal graphs to model social interactions and temporal dependencies. To achieve high-order interaction modelling, we design a higher-order graph attention module to capture pedestrian social and temporal interactions of different orders by stacking multiple layers of graph attention. Subsequently, we design a deformable spatial-temporal sparse module to adaptively eliminate social and temporal redundant interactions. To balance deterministic and multimodal prediction performance, we design a two-stage prediction strategy. The first stage predicts pedestrian deterministic trajectories, and the second stage refines pedestrian deterministic trajectories to complete both deterministic and multimodal predictions. Quantitative analysis on the ETH, UCY, and SDD datasets demonstrates that our method outperforms existing methods in both deterministic and multimodal predictions. Qualitative analysis shows that our method can effectively describe complex social relationships and accomplish reliable trajectory prediction.