# Beyond MSE: Rethinking the Evaluation Metric and Benchmarking for Irregular Time Series Forecasting

arXiv: https://arxiv.org/abs/2608.17293 · HTML: https://mlsanity.com/paper/2608.17293/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 26 references that are in the map.
- First posted on arXiv 18 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Multi-Time Attention Networks for Irregularly Sampled Time Series](https://mlsanity.com/paper/2101.10318/) (2021)
- [Set Functions for Time Series](https://mlsanity.com/paper/1909.12064/) (2019)
- [Graph-Guided Network for Irregularly Sampled Multivariate Time Series](https://mlsanity.com/paper/2110.05357/) (2021)
- [Modeling Irregular Time Series with Continuous Recurrent Units](https://mlsanity.com/paper/2111.11344/) (2021)
- [Neural Flows: Efficient Alternative to Neural ODEs](https://mlsanity.com/paper/2110.13040/) (2021)
- [Warpformer: A Multi-scale Modeling Approach for Irregular Clinical Time Series](https://mlsanity.com/paper/2306.09368/) (2023)
- [Rethinking Irregular Time Series Forecasting: A Simple yet Effective Baseline](https://mlsanity.com/paper/2505.11250/) (2025)
- [Physiome-ODE: A Benchmark for Irregularly Sampled Multivariate Time Series Forecasting Based on Biological ODEs](https://mlsanity.com/paper/2502.07489/) (2025)
- [PYRREGULAR: A Unified Framework for Irregular Time Series, with Classification Benchmarks](https://mlsanity.com/paper/2505.06047/) (2025)
- [Revitalizing Canonical Pre-Alignment for Irregular Multivariate Time Series Forecasting](https://mlsanity.com/paper/2508.01971/) (2025)
- [Benchmarking with MIMIC-IV, an irregular, spare clinical time series dataset](https://mlsanity.com/paper/2401.15290/) (2024)

## Abstract (arXiv)

Existing research on irregular time-series forecasting has primarily focused on model design, while evaluation metrics remain insufficiently studied. Existing benchmarks typically use mean squared error (MSE) as the evaluation metric. We show that, in irregular forecasting, MSE is determined not only by the model prediction but also by the sample-specific timestamp sampling distributions, leading to a biased assessment of the models' continuous-time predictive performance. To address this issue, we propose the Continuous-time Squared Error (CSE), which employs importance weighting to eliminate the influence of the timestamp sampling distributions. We further theoretically prove that CSE's asymptotic estimation error with respect to continuous-time risk is no greater than that of MSE. Finally, we construct a systematic benchmark covering synthetic, semi-synthetic, and eight real-world datasets to validate the effectiveness of CSE and systematically evaluate models' continuous-time predictive performance. Experiments show that CSE can recover continuous-time risk more accurately than MSE, while relying solely on MSE may not fully reflect models' continuous-time predictive performance in real-world scenarios. Our code can be obtained at https://github.com/hnu-vis/ITS-Bench.