# A Hybrid Loss Framework for Decomposition-based Time Series Forecasting Methods: Balancing Global and Component Errors

arXiv: https://arxiv.org/abs/2411.11340 · HTML: https://mlsanity.com/paper/2411.11340/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 33 references that are in the map.
- First posted on arXiv 18 Nov 2024.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [Monash Time Series Forecasting Archive](https://mlsanity.com/paper/2105.06643/) (2021)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [Less Is More: Fast Multivariate Time Series Forecasting with Light Sampling-oriented MLP Structures](https://mlsanity.com/paper/2207.01186/) (2022)
- [ETSformer: Exponential Smoothing Transformers for Time-series Forecasting](https://mlsanity.com/paper/2202.01381/) (2022)

## Abstract (arXiv)

Accurate time series forecasting, predicting future values based on past data, is crucial for diverse industries. Many current time series methods decompose time series into multiple sub-series, applying different model architectures and training with an end-to-end overall loss for forecasting. However, this raises a question: does this overall loss prioritize the importance of critical sub-series within the decomposition for the better performance? To investigate this, we conduct a study on the impact of overall loss on existing time series methods with sequence decomposition. Our findings reveal that overall loss may introduce bias in model learning, hindering the learning of the prioritization of more significant sub-series and limiting the forecasting performance. To 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 overall loss. It employs a dual min-max algorithm to dynamically adjust weights between the overall loss and component losses, and within component losses. This enables the model to achieve better performance of current time series methods by focusing on more critical sub-series while still maintaining a low overall loss. 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.