Addressing Distribution Shift in Time Series Forecasting with Instance Normalization Flows

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.