CAIFormer: A Causal Informed Transformer for Multivariate Time Series Forecasting

Abstract

Most existing multivariate time series forecasting methods adopt an all-to-all paradigm that feeds all variable histories into a unified model to predict their future values without distinguishing their individual roles. However, this undifferentiated paradigm makes it difficult to identify variable-specific causal influences and often entangles causally relevant information with spurious correlations. To address this limitation, we propose an all-to-one forecasting paradigm that predicts each target variable separately. Specifically, we first construct a Structural Causal Model from observational data and then, for each target variable, we partition the historical sequence into four sub-segments according to the inferred causal structure: endogenous, direct causal, collider causal, and spurious correlation. The prediction relies solely on the first three causally relevant sub-segments, while the spurious correlation sub-segment is excluded. Furthermore, we propose Causal Informed Transformer (CAIFormer), a novel forecasting model comprising three components: Endogenous Sub-segment Prediction Block, Direct Causal Sub-segment Prediction Block, and Collider Causal Sub-segment Prediction Block, which process the endogenous, direct causal, and collider causal sub-segments, respectively. Their outputs are then combined to produce the final prediction. Extensive experiments on multiple benchmark datasets demonstrate the effectiveness of the CAIFormer.