Deep Learning (DL) models can be used to tackle time series analysis tasks with great success. However, the performance of DL models can degenerate rapidly if the data are not appropriately normalized. This issue is even more apparent when DL is used for financial time series forecasting tasks, where the non-stationary and multimodal nature of the data pose significant challenges and severely affect the performance of DL models. In this work, a simple, yet effective, neural layer, that is capable of adaptively normalizing the input time series, while taking into account the distribution of the data, is proposed. The proposed layer is trained in an end-to-end fashion using back-propagation and leads to significant performance improvements compared to other evaluated normalization schemes. The proposed method differs from traditional normalization methods since it learns how to perform normalization for a given task instead of using a fixed normalization scheme. At the same time, it can be directly applied to any new time series without requiring re-training. The effectiveness of the proposed method is demonstrated using a large-scale limit order book dataset, as well as a load forecasting dataset.