High-dimensional Autoregressive Modeling for Time Series with Hierarchical Structures

TL;DR

This paper introduces an interpretable autoregressive model for high-dimensional hierarchical time series, combining factor modeling with OLS estimation, and demonstrates its effectiveness through simulations and real data application.

Contribution

It develops a new framework for modeling high-dimensional hierarchical time series, integrating supervised and unsupervised methods with theoretical guarantees.

Findings

The proposed model performs well in finite samples.

The algorithm effectively estimates hierarchical time series.

Application to Personality-120 dataset shows practical usefulness.

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.