# Temporal Window Smoothing of Exogenous Variables for Improved Time Series Prediction

arXiv: https://arxiv.org/abs/2507.05284 · HTML: https://mlsanity.com/paper/2507.05284/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 31 references that are in the map.
- First posted on arXiv 4 Jul 2025.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (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)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [SimMTM: A Simple Pre-Training Framework for Masked Time-Series Modeling](https://mlsanity.com/paper/2302.00861/) (2023)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark](https://mlsanity.com/paper/2008.08004/) (2020)
- [Neural basis expansion analysis with exogenous variables: Forecasting electricity prices with NBEATSx](https://mlsanity.com/paper/2104.05522/) (2021)
- [Financial Time Series Forecasting using CNN and Transformer](https://mlsanity.com/paper/2304.04912/) (2023)

## Abstract (arXiv)

Although most transformer-based time series forecasting models primarily depend on endogenous inputs, recent state-of-the-art approaches have significantly improved performance by incorporating external information through exogenous inputs. However, these methods face challenges, such as redundancy when endogenous and exogenous inputs originate from the same source and limited ability to capture long-term dependencies due to fixed look-back windows. In this paper, we propose a method that whitens the exogenous input to reduce redundancy that may persist within the data based on global statistics. Additionally, our approach helps the exogenous input to be more aware of patterns and trends over extended periods. By introducing this refined, globally context-aware exogenous input to the endogenous input without increasing the lookback window length, our approach guides the model towards improved forecasting. Our approach achieves state-of-the-art performance in four benchmark datasets, consistently outperforming 11 baseline models. These results establish our method as a robust and effective alternative for using exogenous inputs in time series forecasting.