Title: Supervised Factor Modeling for High-Dimensional Linear Time Series Show Chinese title

Title: 有监督因子建模用于高维线性时间序列

Abstract: Motivated by Tucker tensor decomposition, this paper imposes low-rank structures to the column and row spaces of coefficient matrices in a multivariate infinite-order vector autoregression (VAR), which leads to a supervised factor model with two factor modelings being conducted to responses and predictors simultaneously. Interestingly, the stationarity condition implies an intrinsic weak group sparsity mechanism of infinite-order VAR, and hence a rank-constrained group Lasso estimation is considered for high-dimensional linear time series. Its non-asymptotic properties are discussed thoughtfully by balancing the estimation, approximation and truncation errors. Moreover, an alternating gradient descent algorithm with thresholding is designed to search for high-dimensional estimates, and its theoretical justifications, including statistical and convergence analysis, are also provided. Theoretical and computational properties of the proposed methodology are verified by simulation experiments, and the advantages over existing methods are demonstrated by two real examples. Show Chinese abstract

Abstract: 受Tucker张量分解的启发，本文在多变量无限阶向量自回归（VAR）系数矩阵的列空间和行空间上施加低秩结构，从而得到一个监督因子模型，该模型同时对响应变量和预测变量进行两种因子建模。 有趣的是，平稳性条件暗示了无限阶VAR的内在弱组稀疏机制，因此考虑使用约束秩组Lasso估计方法来处理高维线性时间序列。 通过平衡估计误差、近似误差和截断误差，深入讨论了其非渐近性质。 此外，设计了一种带有阈值的交替梯度下降算法来搜索高维估计，并提供了包括统计分析和收敛性分析在内的理论依据。 通过模拟实验验证了所提出方法的理论和计算性质，并通过两个实际例子展示了其相对于现有方法的优势。