# Long-term Forecasting with TiDE: Time-series Dense Encoder

arXiv: https://arxiv.org/abs/2304.08424 · HTML: https://mlsanity.com/paper/2304.08424/

## Key facts

- Cited by 332 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 37 references that are in the map.
- First posted on arXiv 17 Apr 2023.

## Builds on (most cited first, 19 of 19)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (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)
- [Linformer: Self-Attention with Linear Complexity](https://mlsanity.com/paper/2006.04768/) (2020)
- [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)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Diagonal State Spaces are as Effective as Structured State Spaces](https://mlsanity.com/paper/2203.14343/) (2022)
- [Coupled Oscillatory Recurrent Neural Network (coRNN): An accurate and (gradient) stable architecture for learning long time dependencies](https://mlsanity.com/paper/2010.00951/) (2020)
- [Learning Linear Dynamical Systems via Spectral Filtering](https://mlsanity.com/paper/1711.00946/) (2017)
- [Deep Independently Recurrent Neural Network (IndRNN)](https://mlsanity.com/paper/1910.06251/) (2019)
- [On the benefits of maximum likelihood estimation for Regression and Forecasting](https://mlsanity.com/paper/2106.10370/) (2021)
- [Task-Synchronized Recurrent Neural Networks](https://mlsanity.com/paper/2204.05192/) (2022)

## Built on by (most cited first, 30 of 332)

- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [Titans: Learning to Memorize at Test Time](https://mlsanity.com/paper/2501.00663/) (2024)
- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [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)
- [GIFT-Eval: A Benchmark For General Time Series Forecasting Model Evaluation](https://mlsanity.com/paper/2410.10393/) (2024)
- [Timer: Generative Pre-trained Transformers Are Large Time Series Models](https://mlsanity.com/paper/2402.02368/) (2024)
- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [Sundial: A Family of Highly Capable Time Series Foundation Models](https://mlsanity.com/paper/2502.00816/) (2025)
- [TEMPO: Prompt-based Generative Pre-trained Transformer for Time Series Forecasting](https://mlsanity.com/paper/2310.04948/) (2023)
- [TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis](https://mlsanity.com/paper/2410.16032/) (2024)
- [Is Mamba Effective for Time Series Forecasting?](https://mlsanity.com/paper/2403.11144/) (2024)
- [CALF: Aligning LLMs for Time Series Forecasting via Cross-modal Fine-Tuning](https://mlsanity.com/paper/2403.07300/) (2024)
- [SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters](https://mlsanity.com/paper/2405.00946/) (2024)
- [DUET: Dual Clustering Enhanced Multivariate Time Series Forecasting](https://mlsanity.com/paper/2412.10859/) (2024)
- [CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns](https://mlsanity.com/paper/2409.18479/) (2024)
- [Pathformer: Multi-scale Transformers with Adaptive Pathways for Time Series Forecasting](https://mlsanity.com/paper/2402.05956/) (2024)
- [Moirai-MoE: Empowering Time Series Foundation Models with Sparse Mixture of Experts](https://mlsanity.com/paper/2410.10469/) (2024)
- [UniTS: A Unified Multi-Task Time Series Model](https://mlsanity.com/paper/2403.00131/) (2024)
- [SiMBA: Simplified Mamba-Based Architecture for Vision and Multivariate Time series](https://mlsanity.com/paper/2403.15360/) (2024)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [SOFTS: Efficient Multivariate Time Series Forecasting with Series-Core Fusion](https://mlsanity.com/paper/2404.14197/) (2024)
- [Time-MMD: Multi-Domain Multimodal Dataset for Time Series Analysis](https://mlsanity.com/paper/2406.08627/) (2024)
- [This Time is Different: An Observability Perspective on Time Series Foundation Models](https://mlsanity.com/paper/2505.14766/) (2025)
- [AutoTimes: Autoregressive Time Series Forecasters via Large Language Models](https://mlsanity.com/paper/2402.02370/) (2024)
- [TimeMachine: A Time Series is Worth 4 Mambas for Long-term Forecasting](https://mlsanity.com/paper/2403.09898/) (2024)
- [Scaling Wearable Foundation Models](https://mlsanity.com/paper/2410.13638/) (2024)
- [CARD: Channel Aligned Robust Blend Transformer for Time Series Forecasting](https://mlsanity.com/paper/2305.12095/) (2023)

## Abstract (arXiv)

Recent work has shown that simple linear models can outperform several Transformer based approaches in long term time-series forecasting. Motivated by this, we propose a Multi-layer Perceptron (MLP) based encoder-decoder model, Time-series Dense Encoder (TiDE), for long-term time-series forecasting that enjoys the simplicity and speed of linear models while also being able to handle covariates and non-linear dependencies. Theoretically, we prove that the simplest linear analogue of our model can achieve near optimal error rate for linear dynamical systems (LDS) under some assumptions. Empirically, we show that our method can match or outperform prior approaches on popular long-term time-series forecasting benchmarks while being 5-10x faster than the best Transformer based model.