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arXiv · 2606.05560

Wasserstein Exponential Smoothing for Distributional Time Series Forecasting

Takuo Matsubara·Peiwen Jiang·Minh-Ngoc Tran·Wilson Ye Chen
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Abstract

Distributional time series arise when each temporal observation is a probability distribution rather than a scalar. We propose Wasserstein exponential smoothing (WES), a one-parameter recursive forecasting method for distributional time series on $\mathbb{R}$. The method adapts the practical logic of classical exponential smoothing to probability distributions by updating forecast distributions along Wasserstein geodesics. This yields a simple filter that can be applied directly to empirical distributions without parametric density modeling. We estimate the smoothing parameter by minimizing an in-sample Wasserstein prediction loss and establish consistency under a distributional local-level data-generating process. In applications to high-frequency equity-index return distributions and household electricity-demand distributions, WES attains the lowest one-step-ahead Wasserstein prediction error among existing distributional autoregressive and regression-based benchmarks for all $20$ series considered, and is retained in the $90\%$ model confidence set in every case.

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Takuo Matsubara, Peiwen Jiang, Minh-Ngoc Tran, Wilson Ye Chen. 2026-06-04. Wasserstein Exponential Smoothing for Distributional Time Series Forecasting. https://arxiv.org/abs/2606.05560

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