# Exploring Accuracy Law for Deep Time Series Forecasters: An Empirical Study

arXiv: https://arxiv.org/abs/2510.02729 · HTML: https://mlsanity.com/paper/2510.02729/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 41 references that are in the map.
- First posted on arXiv 3 Oct 2025.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [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)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [GIFT-Eval: A Benchmark For General Time Series Forecasting Model Evaluation](https://mlsanity.com/paper/2410.10393/) (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)
- [TimeMixer++: A General Time Series Pattern Machine for Universal Predictive Analysis](https://mlsanity.com/paper/2410.16032/) (2024)
- [From News to Forecast: Integrating Event Analysis in LLM-Based Time Series Forecasting with Reflection](https://mlsanity.com/paper/2409.17515/) (2024)
- [Qlib: An AI-oriented Quantitative Investment Platform](https://mlsanity.com/paper/2009.11189/) (2020)
- [xPatch: Dual-Stream Time Series Forecasting with Exponential Seasonal-Trend Decomposition](https://mlsanity.com/paper/2412.17323/) (2024)

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

- [STReasoner: Empowering LLMs for Spatio-Temporal Reasoning in Time Series via Spatial-Aware Reinforcement Learning](https://mlsanity.com/paper/2601.03248/) (2026)
- [Position: The Inevitable End of One-Architecture-Fits-All-Domains in Time Series Forecasting](https://mlsanity.com/paper/2602.01736/) (2026)
- [Toward Reasoning-Centric Time-Series Analysis](https://mlsanity.com/paper/2510.13029/) (2025)
- [The Spectrum Is Not Enough: When Context Helps Time-Series Forecasting](https://mlsanity.com/paper/2607.13006/) (2026)
- [A Unified Scaling Law for Time Series Foundation Models](https://mlsanity.com/paper/2610.05269/) (2026)

## Abstract (arXiv)

Deep time series forecasting has emerged as a rapidly growing field in recent years. Despite the exponential growth of community interests, progress on standard benchmarks is often limited to marginal improvements. A common consensus of the community is that time series forecasting inherently faces a non-zero error lower bound due to its partially observable and uncertain nature. However, a fundamental question arises: how to estimate the performance upper bound of deep time series forecasters? We delve into univariate time series forecasting, a prevalent forecasting paradigm spanning traditional statistical models to advanced time series foundation models. Going beyond classical series-wise predictability metrics, we realize that the forecasting performance is highly related to window-wise properties due to the sequence-to-sequence forecasting paradigm of deep time series models and introduce a quantitative measurement of window-wise pattern complexity. Through rigorous statistical analyses over more than 4700 newly trained deep forecasting models, we discover a consistent empirical relationship between the minimum attainable forecasting error of deep models and the complexity of window-wise series patterns, which is termed the accuracy law. We further demonstrate that this empirical finding successfully guides us to identify saturated tasks from widely used benchmarks and derive an effective training strategy for time series foundation models, offering valuable insights for future research.