Supervised Factor Modeling for High-Dimensional Linear Time Series

TL;DR

This paper introduces a supervised factor model for high-dimensional linear time series, leveraging low-rank structures and group Lasso estimation, with theoretical analysis and practical algorithms validated through simulations and real data.

Contribution

It develops a novel supervised factor modeling approach for high-dimensional VARs using low-rank constraints and group Lasso, with theoretical guarantees and an efficient estimation algorithm.

Findings

The method effectively captures low-rank structures in high-dimensional VARs.

Theoretical analysis confirms the estimator's non-asymptotic properties.

Simulation and real data experiments demonstrate superior performance over existing methods.

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.