Hierarchical Time Series Forecasting with Operator-Valued Kernels
Abstract
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.
Related
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- Hyponormal Toeplitz operators with operator valued normal symbols
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BibTeX
@misc{yang2026hierarchical,
title = {{Hierarchical Time Series Forecasting with Operator-Valued Kernels}},
author = {Junjie Yang and Adeline Fermanian and Claire Boyer and Gérard Biau},
howpublished = {HAL},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18196},
eprint = {2610.18196},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05795359v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hierarchical Time Series Forecasting with Operator-Valued Kernels
AU - Junjie Yang
AU - Adeline Fermanian
AU - Claire Boyer
AU - Gérard Biau
PY - 2026
DA - 2026/10/13
PB - HAL
DO - 10.48550/arxiv.2610.18196
UR - https://hal.science/hal-05795359v1
AB - 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.
ER -