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.

翻译：现代应用使得高维数据（尤其是时间依赖性数据）无处不在，且其结构日益复杂，变量间存在层次关系的情况也变得更加常见。然而，现有文献中仍缺乏针对此类数据的监督学习工具。为填补这一空白，我们引入了一个新的模型设计框架，并将其与无监督因子建模工具相结合，为具有层次结构的高维时间序列构建了一个高效且可解释的自回归模型。我们考虑使用普通最小二乘估计，并建立了其非渐近性质。此外，我们提出了一种用于搜索估计值的算法，并建议采用提升方法进行超参数选择。通过仿真实验评估了所提方法的有限样本性能，并通过对Personality-120数据集的应用展示了其实用性。