TimeXer: Empowering Transformers for Time Series Forecasting with
  Exogenous Variables
Yuxuan Wang Haixu Wu Jiaxiang Dong Yong Liu Yunzhong Qiu Haoran Zhang Jianmin Wang Mingsheng Long
Recent studies have demonstrated remarkable performance in time series
forecasting. However, due to the partially-observed nature of real-world
applications, solely focusing on the target of interest, so-called endogenous
variables, is usually insufficient to guarantee accurate forecasting. Notably,
a system is often recorded into multiple variables, where the exogenous series
can provide valuable external information for endogenous variables. Thus,
unlike prior well-established multivariate or univariate forecasting that
either treats all the variables equally or overlooks exogenous information,
this paper focuses on a practical setting, which is time series forecasting
with exogenous variables. We propose a novel framework, TimeXer, to utilize
external information to enhance the forecasting of endogenous variables. With a
deftly designed embedding layer, TimeXer empowers the canonical Transformer
architecture with the ability to reconcile endogenous and exogenous
information, where patch-wise self-attention and variate-wise cross-attention
are employed. Moreover, a global endogenous variate token is adopted to
effectively bridge the exogenous series into endogenous temporal patches.
Experimentally, TimeXer significantly improves time series forecasting with
exogenous variables and achieves consistent state-of-the-art performance in
twelve real-world forecasting benchmarks.