METP: Multi-Granularity Integration of External Covariates for Temporal Point Processes

Abstract Accurate modeling of temporal point processes is critical for reliable event forecasting and informed decision-making. While historical event sequences provide a foundation for intensity estimation, existing approaches often neglect external covariates whose lagged effects impact future intensities across multiple temporal granularities. To address this gap, we propose Multi-Granularity Integration of External Covariates for Temporal Point Processes (METP), a framework for incorporating lagged external influences into intensity modeling. METP extracts periodic structures and decomposes external covariate series into multiple temporal granularities. At each granularity, a lag-aware calibration module is introduced to align covariates with event dynamics. Finally, a hierarchical mixture-of-experts strategy is employed to integrate the multi-granular external covariates with historical event embeddings, enabling a representation of the conditional intensity function with enhanced information. Extensive experiments on public and proprietary datasets demonstrate that METP consistently outperforms existing methods in predictive accuracy.