Endexformer: Hierarchical Endogenous-Exogenous Synergy for Multivariate Time Series Forecasting

Exogenous variables provide complementary information that enhances endogenous representations, thereby facilitating more accurate multivariate time series forecasting (MTSF). However, existing methods typically overlook the synergistic interplay between exogenous and endogenous variables by adopting shallow fusion strategies such as simple concatenation or separate encoding, which fail to capture the dynamic dependencies essential for modeling complex temporal patterns. To address this issue, we propose Endexformer, a novel hierarchical Endogenous-Exogenous modeling framework built upon the Transformer architecture. Specifically, Endexformer adopts a hierarchical architecture to jointly model temporal embeddings of endogenous variables and structural embeddings of exogenous variables, enabling a unified representation of cross-variable dependencies. To capture the fine-grained temporal patterns of endogenous variables, we present a multilevel temporal attention mechanism that leverages variable-level embeddings to adaptively incorporate exogenous information. Furthermore, we design a dynamic interactive attention mechanism that selectively emphasizes informative endogenous and exogenous patterns, mitigating redundancy and preserving semantic integrity in variable representations. Extensive experiments on eight real-world datasets show that Endexformer achieves outstanding performance against competing benchmark approaches in MTSF tasks across various temporal scenarios.