arXiv Statistics ML August 24, 2026 By Takuo Matsubara, Peiwen Jiang, Minh-Ngoc Tran, Wilson Ye Chen

Wasserstein Exponential Smoothing for Distributional Time Series Forecasting

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The paper introduces Wasserstein Exponential Smoothing (WES), a single‑parameter recursive method for forecasting distributional time series on ℝ. WES updates forecast distributions along Wasserstein geodesics, allowing direct application to empirical distributions without parametric modeling. In high‑frequency equity‑index return and household electricity‑demand data, WES achieves the lowest one‑step‑ahead Wasserstein prediction error among existing benchmarks and is retained in the 90% model confidence set for all 20 series examined.

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