Test time adaptation (TTA) has emerged as a promising solution to adapt pre-trained models to new, unseen data distributions using unlabeled target domain data. However, most TTA methods are designed for independent data, often overlooking the time series data and rarely addressing forecasting tasks. This paper presents AdaNODEs, an innovative source-free TTA method tailored explicitly for time series forecasting. By leveraging Neural Ordinary Differential Equations (NODEs), we propose a novel adaptation framework that accommodates the unique characteristics of distribution shifts in time series data. Moreover, we innovatively propose a new loss function to tackle TTA for forecasting tasks. AdaNODEs only requires updating limited model parameters, showing effectiveness in capturing temporal dependencies while avoiding significant memory usage. Extensive experiments with one- and high-dimensional data demonstrate that AdaNODEs offer relative improvements of 5.88\% and 28.4\% over the SOTA baselines, especially demonstrating robustness across higher severity distribution shifts.