# CITRAS: Covariate-Informed Transformer for Time Series Forecasting

arXiv: https://arxiv.org/abs/2503.24007 · HTML: https://mlsanity.com/paper/2503.24007/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 67 references that are in the map.
- First posted on arXiv 31 Mar 2025.

## Builds on (most cited first, 30 of 49)

- [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)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (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)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [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)
- [One Fits All:Power General Time Series Analysis by Pretrained LM](https://mlsanity.com/paper/2302.11939/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [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)
- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)

## Built on by (most cited first, 5 of 5)

- [TiRex-2: Generalizing TiRex to Multivariate Data and Streaming](https://mlsanity.com/paper/2607.01204/) (2026)
- [CITRAS-FM: Tiny Time Series Foundation Model for Covariate-Informed Zero-Shot Forecasting](https://mlsanity.com/paper/2606.10798/) (2026)
- [One-Shot Price Forecasting with Covariate-Guided Experts under Privacy Constraints](https://mlsanity.com/paper/2601.11977/) (2026)
- [Geographically-aware Transformer-based Traffic Forecasting for Urban Motorway Digital Twins](https://mlsanity.com/paper/2602.05983/) (2026)
- [Exogenous Dropout: A Simple, Strong Baseline for Corruption-Robust Time Series Forecasting with Covariates](https://mlsanity.com/paper/2607.05452/) (2026)

## Abstract (arXiv)

In time series forecasting, covariates represent external factors that influence target variables. Some covariates are observable only in the past (observed covariates, such as recorded weather data), while others are known in advance (known covariates, such as calendar events or discount schedules). Although covariates have the potential to enhance forecasting performance, most deep learning-based forecasting models struggle to address the length discrepancy between variables caused by the future portion of known covariates and fail to leverage them flexibly. Moreover, capturing dependencies between target variables and covariates is non-trivial, as models must accurately reflect the local impact of covariates while simultaneously modeling global cross-variate dependencies. To address these challenges, we propose CITRAS, a decoder-only Transformer that flexibly integrates multiple target variables, observed covariates, and known covariates. While preserving strong autoregressive modeling capabilities, CITRAS introduces two novel mechanisms within patch-wise cross-variate attention: Key-Value (KV) Shift and Attention Score Smoothing. KV Shift seamlessly incorporates the future portion of known covariates into the forecasting process by aligning them with target variables based on their concurrent dependencies. Attention Score Smoothing refines locally accurate patch-wise cross-variate dependencies into global variate-level dependencies by smoothing the historical attention scores. Experimentally, CITRAS demonstrates strong performance across a wide range of real-world datasets in both covariate-informed and multivariate settings, showcasing its versatile ability to leverage cross-variate and cross-time dependencies for improved forecasting accuracy.