Addressing Distribution Shift in Time Series Forecasting with Instance
  Normalization Flows
Wei Fan Shun Zheng Pengyang Wang Rui Xie Jiang Bian Yanjie Fu
Due to non-stationarity of time series, the distribution shift problem
largely hinders the performance of time series forecasting. Existing solutions
either fail for the shifts beyond simple statistics or the limited
compatibility with forecasting models. In this paper, we propose a general
decoupled formulation for time series forecasting, with no reliance on fixed
statistics and no restriction on forecasting architectures. Then, we make such
a formulation formalized into a bi-level optimization problem, to enable the
joint learning of the transformation (outer loop) and forecasting (inner loop).
Moreover, the special requirements of expressiveness and bi-direction for the
transformation motivate us to propose instance normalization flows (IN-Flow), a
novel invertible network for time series transformation. Extensive experiments
demonstrate our method consistently outperforms state-of-the-art baselines on
both synthetic and real-world data.