Exponential smoothing (ES) often outperforms other techniques in time series forecasting across a wide range of data-generating processes. While ES has traditionally been applied to time series in $\mathbb{R}$, this paper extends the methodology to distributional time series, where each observation is a probability distribution on $\mathbb{R}$. The primary contribution of this work is twofold. First, we propose a principled and intuitive generalization of ES within the Wasserstein space, which retains the exceptional parsimony of classical ES. Second, we theoretically and empirically demonstrate that the smoothing parameter can be consistently estimated by minimizing a Wasserstein distance. Applications to distributional time series of high-frequency financial returns and household electricity demands confirm the practical effectiveness of our Wasserstein ES model.

翻译：指数平滑法（ES）在广泛的数据生成过程中往往优于其他时间序列预测技术。尽管ES传统上应用于$\mathbb{R}$中的时间序列，但本文将该方法扩展至分布时间序列，其中每个观测值为$\mathbb{R}$上的概率分布。本研究的主要贡献体现在两个方面。首先，我们在Wasserstein空间内提出了一种具有原理性且直观的ES推广方法，该方法保留了经典ES的卓越简约性。其次，我们从理论和实证两方面证明，通过最小化Wasserstein距离可以一致地估计平滑参数。高频金融收益与家庭电力需求的分布时间序列应用案例证实了本文提出的Wasserstein ES模型的实际有效性。