Bridging factor and sparse models

TL;DR

This paper introduces a novel supervised learning approach that combines factor and sparse models through a flexible factor-augmented regression framework, improving interpretability and dependence modeling in high-dimensional data.

Contribution

It proposes a lifting method that unifies factor and sparse models, along with a new test for covariance structure, enhancing model selection and dependence analysis in high-dimensional datasets.

Findings

The method effectively weakens cross-sectional dependence.

The proposed test accurately infers covariance structures.

Simulation and real data applications validate the approach.

Abstract

Factor and sparse models are two widely used methods to impose a low-dimensional structure in high-dimensions. However, they are seemingly mutually exclusive. We propose a lifting method that combines the merits of these two models in a supervised learning methodology that allows for efficiently exploring all the information in high-dimensional datasets. The method is based on a flexible model for high-dimensional panel data, called factor-augmented regression model with observable and/or latent common factors, as well as idiosyncratic components. This model not only includes both principal component regression and sparse regression as specific models but also significantly weakens the cross-sectional dependence and facilitates model selection and interpretability. The method consists of several steps and a novel test for (partial) covariance structure in high dimensions to infer the remaining cross-section dependence at each step. We develop the theory for the model and demonstrate the validity of the multiplier bootstrap for testing a high-dimensional (partial) covariance structure. The theory is supported by a simulation study and applications.