# WAVE: Weighted Autoregressive Varying Gate for Time Series Forecasting

arXiv: https://arxiv.org/abs/2410.03159 · HTML: https://mlsanity.com/paper/2410.03159/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 58 references that are in the map.
- First posted on arXiv 4 Oct 2024.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Rethinking Attention with Performers](https://mlsanity.com/paper/2009.14794/) (2020)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [MaskGIT: Masked Generative Image Transformer](https://mlsanity.com/paper/2202.04200/) (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)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (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)
- [AudioLM: a Language Modeling Approach to Audio Generation](https://mlsanity.com/paper/2209.03143/) (2022)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Gated Linear Attention Transformers with Hardware-Efficient Training](https://mlsanity.com/paper/2312.06635/) (2023)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [Transformer Quality in Linear Time](https://mlsanity.com/paper/2202.10447/) (2022)
- [Mega: Moving Average Equipped Gated Attention](https://mlsanity.com/paper/2209.10655/) (2022)
- [HGRN2: Gated Linear RNNs with State Expansion](https://mlsanity.com/paper/2404.07904/) (2024)

## Built on by (most cited first, 3 of 3)

- [Neural CDEs as Correctors for Learned Time Series Models](https://mlsanity.com/paper/2512.12116/) (2025)
- [Beyond Similarity: Temporal Operator Attention for Time Series Analysis](https://mlsanity.com/paper/2605.11287/) (2026)
- [CAST: Causal Anchored Simplex Transport for Distribution-Valued Time Series](https://mlsanity.com/paper/2605.16919/) (2026)

## Abstract (arXiv)

We propose a Weighted Autoregressive Varying gatE (WAVE) attention mechanism equipped with both Autoregressive (AR) and Moving-average (MA) components. It can adapt to various attention mechanisms, enhancing and decoupling their ability to capture long-range and local temporal patterns in time series data. In this paper, we first demonstrate that, for the time series forecasting (TSF) task, the previously overlooked decoder-only autoregressive Transformer model can achieve results comparable to the best baselines when appropriate tokenization and training methods are applied. Moreover, inspired by the ARMA model from statistics and recent advances in linear attention, we introduce the full ARMA structure into existing autoregressive attention mechanisms. By using an indirect MA weight generation method, we incorporate the MA term while maintaining the time complexity and parameter size of the underlying efficient attention models. We further explore how indirect parameter generation can produce implicit MA weights that align with the modeling requirements for local temporal impacts. Experimental results show that WAVE attention that incorporates the ARMA structure consistently improves the performance of various AR attentions on TSF tasks, achieving state-of-the-art results.