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.
From: Takuo Matsubara [view email]
[v1]
Thu, 4 Jun 2026 01:14:22 UTC (1,075 KB)
[v2]
Fri, 21 Aug 2026 00:52:04 UTC (1,184 KB)
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