Most of current deep learning time series methods relies on seasonal and trend sub-series decomposition with an end-to-end global loss training. However, does this global loss prioritize the critical sub-series within the decomposition for the better performance? To investigate this, we show that the global loss can introduce bias in model training, hindering the ability to prioritize more important sub-series and limiting forecasting performance. To further address this, we propose a hybrid loss framework combining the global and component losses. This framework introduces component losses for each sub-series alongside the original global loss, and employs a dual min-max algorithm to dynamically adjust weights between the global loss and component losses, and within component losses. This enables the model to focus on critical sub-series while maintaining a low global loss, improving performance. We integrate our loss framework into several time series methods and evaluate the performance on multiple datasets. Results show an average improvement of 0.5–2% over existing methods without any modifications to the model architectures.