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arXiv · 2510.24574

DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignment

Hao Wang·Licheng Pan·Yuan Lu·Zhixuan Chu·Xiaoxi Li·Shuting He·Zhichao Chen·Haoxuan Li·Qingsong Wen·Zhouchen Lin
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Abstract

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.

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Hao Wang, Licheng Pan, Yuan Lu, Zhixuan Chu, Xiaoxi Li, Shuting He, Zhichao Chen, Haoxuan Li, Qingsong Wen, Zhouchen Lin. 2025-10-28. DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignment. https://arxiv.org/abs/2510.24574

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