# Addressing Prediction Delays in Time Series Forecasting: A Continuous GRU Approach with Derivative Regularization

arXiv: https://arxiv.org/abs/2407.01622 · HTML: https://mlsanity.com/paper/2407.01622/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 44 references that are in the map.
- First posted on arXiv 29 Jun 2024.

## Builds on (most cited first, 16 of 16)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Shape and Time Distortion Loss for Training Deep Time Series Forecasting Models](https://mlsanity.com/paper/1909.09020/) (2019)
- [Neural Controlled Differential Equations for Online Prediction Tasks](https://mlsanity.com/paper/2106.11028/) (2021)
- [Attentive Neural Controlled Differential Equations for Time-series Classification and Forecasting](https://mlsanity.com/paper/2109.01876/) (2021)
- [EXIT: Extrapolation and Interpolation-based Neural Controlled Differential Equations for Time-series Classification and Forecasting](https://mlsanity.com/paper/2204.08771/) (2022)
- [Unveiling Delay Effects in Traffic Forecasting: A Perspective from Spatial-Temporal Delay Differential Equations](https://mlsanity.com/paper/2402.01231/) (2024)

## Built on by (most cited first, 7 of 7)

- [SDE: A Simplified and Disentangled Dependency Encoding Framework for State Space Models in Time Series Forecasting](https://mlsanity.com/paper/2408.12068/) (2024)
- [Continuous Evolution Pool: Taming Recurring Concept Drift in Online Time Series Forecasting](https://mlsanity.com/paper/2506.14790/) (2025)
- [Uncovering Insights of Compound Flooding with Data-Driven AI](https://mlsanity.com/paper/2506.04281/) (2025)
- [DC-Mamber: A Dual Channel Prediction Model based on Mamba and Linear Transformer for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2507.04381/) (2025)
- [Decomposing the Time Series Forecasting Pipeline: A Modular Approach for Time Series Representation, Information Extraction, and Projection](https://mlsanity.com/paper/2507.05891/) (2025)
- [Multi-Source Dynamic Graph Learning for Compound-Flood Forecasting in Managed Coastal Systems](https://mlsanity.com/paper/2608.01775/) (2026)
- [LLMODE: Aligning ODEs with LLMs via Gated Token Injection for Irregular Spatio-Temporal Forecasting](https://mlsanity.com/paper/2608.29640/) (2026)

## Abstract (arXiv)

Time series forecasting has been an essential field in many different application areas, including economic analysis, meteorology, and so forth. The majority of time series forecasting models are trained using the mean squared error (MSE). However, this training based on MSE causes a limitation known as prediction delay. The prediction delay, which implies the ground-truth precedes the prediction, can cause serious problems in a variety of fields, e.g., finance and weather forecasting -- as a matter of fact, predictions succeeding ground-truth observations are not practically meaningful although their MSEs can be low. This paper proposes a new perspective on traditional time series forecasting tasks and introduces a new solution to mitigate the prediction delay. We introduce a continuous-time gated recurrent unit (GRU) based on the neural ordinary differential equation (NODE) which can supervise explicit time-derivatives. We generalize the GRU architecture in a continuous-time manner and minimize the prediction delay through our time-derivative regularization. Our method outperforms in metrics such as MSE, Dynamic Time Warping (DTW) and Time Distortion Index (TDI). In addition, we demonstrate the low prediction delay of our method in a variety of datasets.