For the time series forecasting task, several state-of-the-art algorithms employ moving-average decomposition for improved accuracy. However, the potential of decomposition techniques to enhance time series forecasting methods has not been explored in detail. In this work, we comprehensively investigate the use of decomposition methods for the forecasting task, comparing different decomposition techniques and their effect on forecasting accuracy, as well as the possibility of providing model-agnostic interpretability. We rework recent forecasting models to be compatible with any decomposition technique and experimentally evaluate their effectiveness in different forecasting setups. We further propose and assess a model-agnostic framework using decomposition for interpretability. Our results show that decomposition can improve forecasting accuracy, especially for the proposed decomposition-adapted models. Additionally, we demonstrate that the architectural choices of existing forecasting models can be improved by using different decomposition blocks internally. We found that decomposition techniques must be configured with a low number of components to provide model-agnostic interpretability. Our work concludes that decomposition can enhance time series forecasting algorithms, improving both their performance and interpretability.