High-dimensional Autoregressive Modeling for Time Series with Hierarchical Structures
Abstract
Modern applications have made ubiquitous high-dimensional data, especially time-dependent data, with more and more complicated structures, and it also has become more frequent to encounter the scenario of hierarchical relationships among variables. However, there is still a lack of supervised learning tool in the literature for them. To fill this gap, we introduce a new model-designing framework, and it then combines with unsupervised factor modeling tools to form an efficient and interpretable autoregressive model for high-dimensional time series with hierarchical structures. An ordinary least squares estimation is considered, and its non-asymptotic properties are established. Moreover, we propose an algorithm to search for estimates, and a boosting method is also suggested for hyperparameter selection. Simulation experiments are conducted to evaluate finite-sample performance of the proposed methodology, and its usefulness is demonstrated by an application to the Personality-120 dataset.
Cite
@article{arxiv.2512.00508,
title = {High-dimensional Autoregressive Modeling for Time Series with Hierarchical Structures},
author = {Lan Li and Shibo Yu and Yingzhou Wang and Guodong Li},
journal= {arXiv preprint arXiv:2512.00508},
year = {2026}
}