<p>Time series forecasting plays a crucial role in various fields including network traffic prediction and energy system forecasting. The primary challenge in long-term forecasting is temporal covariate shift (TCS) caused by dynamic changes in time series data. While numerous time series forecasting models have been successfully developed, most focus on learning complex patterns from historical data and lack the ability to dynamically adapt to future distribution shifts. Existing online adaptation methods, primarily designed for image classification tasks, are unsuitable for time series forecasting which requires rapid adaptation to small samples of rapidly changing time series data. In this work, we propose an Online Adaptive Network with Distribution Awareness (OAN-DA) framework. By pretraining a domain encoder to capture target domain distributions and utilizing domain embeddings to guide predictor adjustments, OAN-DA effectively adapts to continuously evolving target distributions using limited target samples. Experimental results demonstrate that when applied to various time series forecasting methods, OAN-DA achieves average performance improvements across three public datasets, reducing Mean Squared Error (MSE) by 61.8%, 65.2%, and 54.17% respectively, highlighting its superior generalization and online adaptation capabilities across temporal and spatial domains.</p>