Forecasting relations between entities is paramount in the current era of data and AI. However, it is often overlooked that real-world relationships are inherently directional, involve more than two entities, and can change with time. In this paper, we provide a comprehensive solution to the problem of forecasting directional relations in a general setting, where relations are higher-order, i.e., directed hyperedges in a hypergraph. This problem has not been previously explored in the existing literature. The primary challenge in solving this problem is that the number of possible hyperedges is exponential in the number of nodes at each event time. To overcome this, we propose a sequential generative approach that segments the forecasting process into multiple stages, each contingent upon the preceding stages, thereby reducing the search space involved in predictions of hyperedges. The first stage involves a temporal point process-based node event forecasting module that identifies the subset of nodes involved in an event. The second stage is a candidate generation module that predicts hyperedge sizes and adjacency vectors for nodes observing events. The final stage is a directed hyperedge predictor that identifies the truth by searching over the set of candidate hyperedges. To validate the effectiveness of our model, we compiled five datasets and conducted an extensive empirical study to assess each downstream task. Our proposed method achieves a performance gain of 32\% and 41\% compared to the state-of-the-art pairwise and hyperedge event forecasting models, respectively, for the event type prediction.

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