DAG: A Dual Causal Network for Time Series Forecasting with Exogenous Variables

Time series forecasting is crucial in various fields such as economics, traffic, and AIOps. However, in real-world applications, focusing solely on the endogenous variables (i.e., target variables), is often insufficient to ensure accurate predictions. Considering exogenous variables (i.e., covariates) provides additional predictive information, thereby improving forecasting accuracy. However, existing methods for time series forecasting with exogenous variables (TSF-X) have the following shortcomings: 1) they do not leverage future exogenous variables, 2) they fail to account for the causal relationships between endogenous and exogenous variables. As a result, their performance is suboptimal. In this study, to better leverage exogenous variables, especially future exogenous variable, we propose a general framework DAG, which utilizes dual causal network along both the temporal and channel dimensions for time series forecasting with exogenous variables. Specifically, we first introduce the Temporal Causal Module, which includes a causal discovery module to capture how historical exogenous variables affect future exogenous variables. Following this, we construct a causal injection module that incorporates the discovered causal relationships into the process of forecasting future endogenous variables based on historical endogenous variables. Next, we propose the Channel Causal Module, which follows a similar design principle. It features a causal discovery module models how historical exogenous variables influence historical endogenous variables, and a causal injection module incorporates the discovered relationships to enhance the prediction of future endogenous variables based on future exogenous variables.