cs.LGAug 18, 2026

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

Authors: Rongwen Li, Haixin Xie, Xiao Wang, Changjian Chen

Organizations: College of Computer Science and Electronic Engineering, Hunan University, Changsha, Hunan, China.

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Abstract

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.

Figures & tables

Figure 1: Illustration of evaluation bias under non-uniform sampling. Although Model B has lower continuous-time error, Model A obtains a lower MSE because of over-dense sampling within the interval [0.0,0.4][0.0,0.4] .
Figure 2: Normalized decomposition of the evaluation discrepancy into the sampling-dependence gap G^samp\widehat{G}_{\mathrm{samp}} and temporal-distribution gap G^time\widehat{G}_{\mathrm{time}} across models and datasets.
Figure 3: Model ranking changes when replacing MSE with CSE on eight real-world datasets. Panel (a) reports the number of pairwise rank inversions, while Panel (b) compares the frequency with which each model is ranked first.
Figure 4: Relative errors of MSE and CSE with respect to RctR_{\mathrm{ct}} under increasing sampling non-uniformity.
Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Figure 5: Relative estimation errors of MSE and CSE with respect to RctR_{\mathrm{ct}} under increasing sampling non-uniformity on all synthetic and semi-synthetic datasets.

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