Supervised factor modeling for high-dimensional linear time series

IF 9.9 3区 经济学 Q1 ECONOMICS
Feiqing Huang , Kexin Lu , Yao Zheng , Guodong Li
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引用次数: 0

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 by balancing the estimation, approximation and truncation errors. Moreover, an alternating gradient descent algorithm with hard-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 analyzing US quarterly macroeconomic variables.
高维线性时间序列的监督因子建模
基于Tucker张量分解,在多元无穷阶向量自回归(VAR)中,对系数矩阵的列空间和行空间施加低秩结构,从而得到一个同时对响应和预测者进行两因素建模的监督因子模型。有趣的是,平稳性条件暗示了无限阶VAR固有的弱群稀疏性机制,因此考虑了高维线性时间序列的秩约束群Lasso估计。通过平衡估计误差、近似误差和截断误差,讨论了其非渐近性质。此外,设计了一种带有硬阈值的交替梯度下降算法来搜索高维估计,并给出了该算法的理论依据,包括统计分析和收敛分析。通过模拟实验验证了所提方法的理论和计算特性,并通过分析美国季度宏观经济变量证明了其优于现有方法的优势。
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来源期刊
Journal of Econometrics
Journal of Econometrics 社会科学-数学跨学科应用
CiteScore
8.60
自引率
1.60%
发文量
220
审稿时长
3-8 weeks
期刊介绍: The Journal of Econometrics serves as an outlet for important, high quality, new research in both theoretical and applied econometrics. The scope of the Journal includes papers dealing with identification, estimation, testing, decision, and prediction issues encountered in economic research. Classical Bayesian statistics, and machine learning methods, are decidedly within the range of the Journal''s interests. The Annals of Econometrics is a supplement to the Journal of Econometrics.
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