The Continuous-time Squared Error (CSE) is proposed, which employs importance weighting to eliminate the influence of the timestamp sampling distributions and theoretically proves that CSE's asymptotic estimation error with respect to continuous-time risk is no greater than that of MSE.
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.
As time-series foundation models have emerged, the need for benchmarks that can evaluate their forecasting ability in meaningful ways has become increasingly important. Existing time-series forecasting benchmarks provide useful standardized comparisons, but they often evaluate heterogeneous series with uniform error-based metrics. Strong performance under such metrics does not necessarily imply that a model's forecasts will support the best real-world decisions across domains. For example, in stock forecasting, correctly predicting whether a price will rise or fall can be more directly relevant to realized returns than minimizing point-wise forecast error alone. To this end, we introduce FinVerse, a finance-domain time-series forecasting benchmark that takes a first step toward more realistic evaluation. The released FinVerse data artifact contains 116,897 financial time series with 171.1M observations, of which 60,232 series with 17.4M observations are selected as evaluated targets based on their economic relevance to financial decisions. Unlike generic forecasting benchmarks that primarily emphasize uniform point-forecast or probabilistic accuracy, FinVerse defines 11 metric families comprising 78 evaluation metrics and assigns the most appropriate evaluation metrics to each individual time series based on its underlying economic meaning. Our analysis of 43 public time-series forecasting foundation models shows that strong performance under generic forecasting criteria does not necessarily translate into useful financial forecasts. This finding highlights the need for domain-aware benchmarks that evaluate models under objectives closer to real-world decision making.
Jaehoon Lee, Jun Seo, Seunghan Lee et al.· 0 citations
Industrial monitoring models must detect operationally relevant deviations while satisfying target-specific data, calibration, and resource constraints. Time-series foundation models (TSFMs) promise reusable representations and zero-shot forecasts, yet evidence for their deployment value remains mixed when task definitions are heterogeneous and lightweight baselines are competitive. This work presents a protocol-aware empirical assessment across three settings: a C-MAPSS degradation-risk proxy, normal-only training for anomalous-sound detection on MIMII, and BDG2 forecasting-residual diagnostics with synthetic target perturbations. We assess classical one-class methods, compact neural autoencoders, residual forecasters, MOMENT-small, Chronos-T5, and TimesFM 2.5 in terms of anomaly-ranking performance, risk-horizon sensitivity, residual forecasting and perturbation sensitivity, and local implementation cost. Across 100 C-MAPSS engines evaluated out of fold, TCN-AE reaches fold-weighted AUROC/AUPRC 0.9570/0.8960, compared with 0.7310/0.3080 for MOMENT reconstruction; paired engine-cluster bootstrap confidence intervals exclude zero for both differences. Across five matched MIMII pump evaluations, OCSVM also exceeds MOMENT reconstruction in AUROC and AUPRC. On a fixed 12-meter BDG2 panel, TimesFM 2.5 has the lowest aligned forecast error and the highest synthetic AUROC point estimate, although synthetic AUPRC is similar across TSFM and fitted residual models. Same-device measurements show that MOMENT incurs higher latency, peak allocated VRAM, and serialized state-dictionary size than TCN-AE. Under the evaluated frozen and zero-shot settings, TSFMs are task-dependent deployment options rather than default replacements for fitted lightweight models.
Irregular time series forecasting is crucial in many domains, such as healthcare and meteorological observation. However, due to the inherent characteristics of irregular time series, including sparse observations and non-uniform sampling, accurately predicting future dynamics remains challenging. In light of these two characteristics, many existing methods aggregate irregular observations into fixed-dimensional estimated response coefficients through predefined basis functions and use these coefficients as sequence representations. Nevertheless, this modeling paradigm still suffers from two key limitations: (i) a potential non-vanishing asymptotic bias caused by ignoring the sampling density of timestamps; and (ii) the limited adaptability of predefined basis functions to diverse temporal patterns. In this study, we propose a Debiased Neural Basis-Function Network (DNBNet) to address these challenges. Its core is a debiased neural basis-function response mechanism, which corrects asymptotic bias through importance sampling while parameterizing basis functions with neural networks to adapt to diverse temporal patterns. In addition, considering the sparsity of irregular data, we design a novel multi-scale decomposition module based on average pooling, together with a mass-aware fusion mechanism, to obtain richer representations. Finally, a dual-branch decoder is employed for forecasting. Extensive experiments on multiple real-world datasets demonstrate the effectiveness of DNBNet and its strong generalizability across diverse irregular time series scenarios. Our code can be obtained at https://github.com/hnu-vis/DNBNet.
This work proposes CvLoss, a plug-in structural regularizer that constrains forecast residuals on a cross-variable graph and shows that CvLoss consistently improves competitive forecasting models, outperforms representative learning objectives, and is compatible with a variety of forecasting backbones.
Kuiye Ding, Yifan Hu, Hanchen Wang et al.· 0 citations
We develop a non-parametric approach to refine forecast-error histories for safety stock estimation without relying on error magnitude or recency alone. Using forecast-error data from a fast-moving consumer goods environment, we show that one year of errors is insufficient to characterize service-level risk, while pooling several years is problematic because error distributions change over time. Non-parametric annual comparisons indicate a progressive reduction in bias and dispersion, consistent with learning in the forecasting process. We propose LOWDII (Leave-One-Out Wasserstein Distributional Influence Index), a diagnostic that evaluates the distributional influence of each historical forecast error on the empirical uncertainty distribution used for safety stock calibration. LOWDII identifies observations whose influence is disproportionate to their representativeness, separating transient distortions from persistent tail behaviour without imposing parametric assumptions. We evaluate the method in a discrete-event simulation using subsequent-year demand realizations as validation. The results show that LOWDII achieves the target service level while reducing average stock by 5.1% to 22.6% relative to benchmark methods. From a managerial perspective, LOWDII helps firms translate improvements in the forecasting process into safety stock decisions, avoiding the projection of obsolete historical errors into the future and capturing the economic benefit of lower uncertainty requirements earlier.
Luis Fernández-Palacios, M. Ceballos, Yolanda Muñoz-Ocaña· 0 citations
Long-term time series forecasting benefits from preserving global structure such as trends and seasonality. Recent LLM-based forecasters often improve accuracy through test-time scaling (e.g., iterative refinement), but these methods are computationally expensive and increasingly prone to global-shape mismatch as the prediction horizon extends. We propose SCALER, a coarse-to-fine forecasting framework that first employs a lightweight Transformer tailored to long-term shape modeling to predict a coarse representation of future dynamics. This predicted shape then serves as a compact guide for an LLM to perform test-time scaling via iterative coarse-to-fine residual token refinement, while processing substantially fewer tokens at each step. By guiding refinement with an explicit future-shape prediction, SCALER reduces reliance on long description prompts, and its fixed-step refinement avoids costly reward-model-based selection, further lowering computational overhead. Experimental results demonstrate that SCALER outperforms strong forecasting baselines in long-term, short-term and zero-shot forecasting while significantly reducing the inference cost associated with scaled LLM for time series forecasting. Code: https://github.com/xuanmay2701/SCALER.
Xuan-May Le, Minh-Tuan Tran, Ling Luo et al.· Proceedings of the 32nd ACM...· 0 citations
