Deep learning approaches are increasingly used to tackle forecasting tasks. A key factor in the successful application of these methods is a large enough training sample size, which is not always available. In these scenarios, synthetic data generation techniques are usually applied to augment the dataset. Data augmentation is typically applied before fitting a model. However, these approaches create a single augmented dataset, potentially limiting their effectiveness. This work introduces OnDAT (On-the-fly Data Augmentation for Time series) to address this issue by applying data augmentation during training and validation. Contrary to traditional methods that create a single, static augmented dataset beforehand, OnDAT performs augmentation on-the-fly. By generating a new augmented dataset on each iteration, the model is exposed to a constantly changing augmented data variations. We hypothesize this process enables a better exploration of the data space, which reduces the potential for overfitting and improves forecasting performance. We validated the proposed approach using a state-of-the-art deep learning forecasting method and 8 benchmark datasets containing a total of 75797 time series. The experiments suggest that OnDAT leads to better forecasting performance than a strategy that applies data augmentation before training as well as a strategy that does not involve data augmentation. The method and experiments are publicly available.