Deep Time-series Forecasting Needs Kernelized Moment Balancing

Training time-series forecasting models requires aligning the conditional distribution of model forecasts with that of the label sequence. The standard direct forecast (DF) approach resorts to minimizing the conditional negative log-likelihood, typically estimated by the mean squared error. However, this estimation proves biased when the label sequence exhibits autocorrelation. In this paper, we propose DistDF, which achieves alignment by minimizing a distributional discrepancy between the conditional distributions of forecast and label sequences. Since such conditional discrepancies are difficult to estimate from finite time-series observations, we introduce a joint-distribution Wasserstein discrepancy for time-series forecasting, which provably upper bounds the conditional discrepancy of interest. The proposed discrepancy is tractable, differentiable, and readily compatible with gradient-based optimization. Extensive experiments show that DistDF improves diverse forecasting models and achieves leading performance. Code is available at https://anonymous.4open.science/r/DistDF-F66B.

Time series forecasting is critical across finance, healthcare, and cloud computing, yet progress is constrained by a fundamental bottleneck: the scarcity of large-scale, high-quality benchmarks. To address this gap, we introduce QuitoBench, a regime-balanced benchmark for time series forecasting with coverage across eight trend$\times$seasonality$\times$forecastability (TSF) regimes, designed to capture forecasting-relevant properties rather than application-defined domain labels. The benchmark is built upon Quito, a billion-scale time series corpus of application traffic from Alipay spanning nine business domains. Benchmarking 10 models from deep learning, foundation models, and statistical baselines across 232,200 evaluation instances, we report four key findings: (i) a context-length crossover where deep learning models lead at short context ($L=96$) but foundation models dominate at long context ($L \ge 576$); (ii) forecastability is the dominant difficulty driver, producing a $3.64 \times$ MAE gap across regimes; (iii) deep learning models match or surpass foundation models at $59 \times$ fewer parameters; and (iv) scaling the amount of training data provides substantially greater benefit than scaling model size for both model families. These findings are validated by strong cross-benchmark and cross-metric consistency. Our open-source release enables reproducible, regime-aware evaluation for time series forecasting research.

Reliable long-horizon time series forecasting is an important yet difficult problem. Trends and seasonality introduce complex temporal structure that challenges learning-based forecasting models. Differencing, which subtracts nearby past values to remove such structure, is the classical remedy, but its reliance on hand-picked orders and periods has kept it largely absent from recent deep architectures. We propose Adaptive Reversible Differencing (AdaRDiff), a generalized differencing approach that uses learnable weights to simplify the series through weighted differencing with previous time instants. This yields stabilized residuals on which forecasting is performed, after which the removed components are restored autoregressively to reconstruct the forecast, capturing trend and seasonality jointly through a single operator. This reconstruction admits a closed-form convolutional expression, which parallelizes on GPU and yields up to $33.7\times$ speedup over the naive recurrence. We furthermore rely on a two-phase training schedule that separates temporal structure discovery from reconstruction learning, as suggested by a theoretical analysis of the gradient when using a linear forecasting model. AdaRDiff attains state-of-the-art forecast accuracy across eight benchmarks spanning electricity, weather, traffic, and energy, at negligible parameter cost. Furthermore, it is designed as a plug-and-play module: integrating AdaRDiff improves eight diverse backbones, from linear models to Transformers, in the large majority of cases, by up to $25.9\%$ with a linear backbone and $18.3\%$ with iTransformer.