  It is imperative to discern the relationships between multiple time series
for accurate forecasting. In particular, for stock prices, components are often
divided into groups with the same characteristics, and a model that extracts
relationships consistent with this group structure should be effective. Thus,
we propose the concept of hierarchical permutation-equivariance, focusing on
index swapping of components within and among groups, to design a model that
considers this group structure. When the prediction model has hierarchical
permutation-equivariance, the prediction is consistent with the group
relationships of the components. Therefore, we propose a hierarchically
permutation-equivariant model that considers both the relationship among
components in the same group and the relationship among groups. The experiments
conducted on real-world data demonstrate that the proposed method outperforms
existing state-of-the-art methods.
