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

Despite recent progress in irregular time series forecasting, the field still lacks a unified benchmark for fair and comprehensive evaluation. Existing evaluations are often conducted on a limited set of datasets with inconsistent experimental protocols and predominantly error-based metrics, rendering it difficult to compare and assess methods fairly and comprehensively across diverse settings. To eliminate these limitations and accelerate progress, we propose BITS, a standardized, reproducible, and extensible benchmark for advancing research on irregular time series forecasting. BITS covers eleven datasets from nine domains with diverse irregularity characteristics, and it characterizes the datasets according to their missing rate, missing pattern complexity, sampling irregularity, and skewness. Further, it offers a unified pipeline for data preprocessing, model integration and evaluation, and reporting. It accommodates regular and irregular time series forecasting methods, including time series foundation models, under consistent settings, incorporating both error-based and non-error-based evaluation metrics. Findings include that method performance varies substantially across irregularity characteristics, with no single modeling strategy consistently dominating. We also find that using error-based or non-error-based metrics can yield different model rankings, highlighting the need for multi-dimensional evaluation. The code can be found at https://anonymous.4open.science/r/BITS-8F2E/.

Irregular multivariate time series are widely encountered in applications such as healthcare monitoring, human activity recognition, and environmental sensing. Their core challenges stem from asynchronous observations, non-uniform sampling intervals, and the fact that temporal patterns themselves carry critical dynamic information. Existing approaches either rely on discretization-based preprocessing (e.g., interpolation, imputation, or aggregation), which disrupts the underlying continuous-time semantics, or adopt continuous-time modeling via ODE-based frameworks, which typically require specialized architectures and incur substantial computational overhead due to numerical solvers. To address these limitations, we propose WrapFlow, a continuous-time modeling framework for irregular time series forecasting. On the input side, WrapFlow introduces Continuous-Time Tokenization, which directly encodes raw observation events and explicitly models long unobserved intervals via gap-aware tokens. The resulting continuous-time tokens are then processed by a standard Transformer backbone to capture long-range temporal dependencies. On the output side, we develop a simulation-free training paradigm for Residual Flow Matching, which learns conditional residual vector fields around base predictions while avoiding numerical-solver simulation and backpropagation during training. This design enables high-quality continuous forecasting using only a small number of fixed rollout steps at inference. Extensive experiments on multiple real-world datasets demonstrate that WrapFlow achieves state-of-the-art performance.

Multi-step time series forecasting (MSF) is commonly evaluated using point-wise error metrics such as mean squared error (MSE), implicitly treating the conditional mean as a sufficient target. We show that this can be misleading under conditional uncertainty, where the conditional expectation becomes unrepresentative of typical realized values at longer horizons. We formalize this effect through a conditional uncertainty gap and prove that whenever this gap is nonzero, no deterministic predictor can simultaneously minimize MSE and match the marginal distribution of realized futures. This establishes a fundamental, model-agnostic trade-off between point accuracy and marginal realism in MSF evaluation. Using controlled stochastic dynamical systems and nine real-world forecasting benchmarks, we empirically characterize the resulting accuracy--realism frontier and \textbf{quantify the practical cost of MSE-only model selection}. As conditional uncertainty increases with forecast horizon, the attainable set expands into a pronounced Pareto front, separating MSE-optimal but under-dispersed predictors from methods that trade accuracy for realistic marginal variability. \textbf{Across benchmarks, we find that small relaxations in MSE ($\boldsymbol{\le 5\%}$) frequently unlock disproportionate gains in marginal realism, with median improvements of $\mathbf{17.3\%}$ and gains exceeding $\mathbf{30\%}$ in some datasets.} We further show that common forecasting strategies systematically occupy different regions of this frontier: direct multi-output predictors concentrate near the accuracy-optimal extreme, while recursive strategies and sample-based inference favors marginal realism. Together, these results expose a structural failure mode of MSE-based evaluation in long-horizon forecasting and recast strategy and inference selection as navigation of an unavoidable accuracy--realism trade-off.