Supervised factor modeling for high-dimensional linear time series

Feiqing Huang, Kexin Lu, Yao Zheng and Guodong Li

Journal of Econometrics, 2025, vol. 249, issue PB

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.

Keywords: Dimension reduction; High-dimensional time series; Infinite-order VAR; Tensor decomposition; Weak group sparsity (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:249:y:2025:i:pb:s0304407625000491

DOI: 10.1016/j.jeconom.2025.105995

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