# Hierarchical Time Series Forecasting with Operator-Valued Kernels

arXiv: https://arxiv.org/abs/2610.18196 · HTML: https://mlsanity.com/paper/2610.18196/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 53 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 13 of 13)

- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [FALKON: An Optimal Large Scale Kernel Method](https://mlsanity.com/paper/1705.10958/) (2017)
- [Operator-valued Kernels for Learning from Functional Response Data](https://mlsanity.com/paper/1510.08231/) (2015)
- [Preconditioning Kernel Matrices](https://mlsanity.com/paper/1602.06693/) (2016)
- [A machine learning approach for forecasting hierarchical time series](https://mlsanity.com/paper/2006.00630/) (2020)
- [Graph-based Time Series Clustering for End-to-End Hierarchical Forecasting](https://mlsanity.com/paper/2305.19183/) (2023)
- [A Unifying Framework in Vector-valued Reproducing Kernel Hilbert Spaces for Manifold Regularization and Co-Regularized Multi-view Learning](https://mlsanity.com/paper/1401.8066/) (2014)
- [HierarchicalForecast: A Reference Framework for Hierarchical Forecasting in Python](https://mlsanity.com/paper/2207.03517/) (2022)
- [SLOTH: Structured Learning and Task-based Optimization for Time Series Forecasting on Hierarchies](https://mlsanity.com/paper/2302.05650/) (2023)
- [Nonlinear Functional Output Regression: a Dictionary Approach](https://mlsanity.com/paper/2003.01432/) (2020)
- [Hierarchical Demand Forecasting Benchmark for the Distribution Grid](https://mlsanity.com/paper/1910.03976/) (2019)
- [Forecasting time series with constraints](https://mlsanity.com/paper/2502.10485/) (2025)

## Abstract (arXiv)

Hierarchical time series forecasting requires generating accurate predictions that are coherent across multiple levels of aggregation. Existing methods either rely on two-stage pipelines with post-hoc reconciliation or on end-to-end models that often lack statistical guarantees. We introduce a unified framework that formulates hierarchical forecasting as a multivariate regression problem in a vector-valued reproducing kernel Hilbert space. By designing structured operator-valued kernels, our approach enforces coherence directly within the hypothesis space, ensuring that all predictions satisfy hierarchical constraints by construction. We further propose tailored kernel constructions for hierarchical data and derive excess risk bounds that characterize generalization performance. Empirical results on synthetic and real-world datasets demonstrate the relevance of the proposed method.