Deep time series forecasting has emerged as a booming direction in recent years. Despite the exponential growth of community interests, researchers are sometimes confused about the direction of their efforts due to minor improvements on standard benchmarks. In this paper, we notice that, unlike image recognition, whose well-acknowledged and realizable goal is 100% accuracy, time series forecasting inherently faces a non-zero error lower bound due to its partially observable and uncertain nature. To pinpoint the research objective and release researchers from saturated tasks, this paper focuses on a fundamental question: how to estimate the performance upper bound of deep time series forecasting? Going beyond classical series-wise predictability metrics, e.g., ADF test, we realize that the forecasting performance is highly related to window-wise properties because of the sequence-to-sequence forecasting paradigm of deep time series models. Based on rigorous statistical tests of over 2,800 newly trained deep forecasters, we discover a significant exponential relationship between the minimum forecasting error of deep models and the complexity of window-wise series patterns, which is termed the accuracy law. The proposed accuracy law successfully guides us to identify saturated tasks from widely used benchmarks and derives an effective training strategy for large time series models, offering valuable insights for future research. Despite these advancements, we notice that the latest proposed models have shown minor improvements on existing widely used benchmarks. As presented in Figure 1, the improvement in the performance of deep time series models on four standard benchmarks has slowed significantly over the past three years. For instance, on the ETT benchmark (Zhou et al., 2021), the relative forecasting performance improvements exhibited a continuous downward trend from 2022 to 2025, with values of 14.98%, 7.77%, 3.93%, and 3.51% respectively.

Recently, time series foundation models have shown promising zero-shot forecasting performance on time series from a wide range of domains. However, it remains unclear whether their success stems from a true understanding of temporal dynamics or simply from memorizing the training data. While implicit reasoning in language models has been studied, similar evaluations for time series models have been largely unexplored. This work takes an initial step toward assessing the reasoning abilities of deep time series forecasting models. We find that certain linear, MLP-based, and patch-based Transformer models generalize effectively in systematically orchestrated out-of-distribution scenarios, suggesting underexplored reasoning capabilities beyond simple pattern memorization.