Sparse factor models of high dimension

TL;DR

This paper introduces a penalized estimation approach for high-dimensional sparse factor models, demonstrating theoretical consistency and practical effectiveness in finance and macroeconomics applications.

Contribution

It develops a novel penalized M-estimation method for sparse factor models with broad sparsity patterns and proves its sparsistency in high-dimensional settings.

Findings

The estimator is consistent and correctly recovers zero entries in the loading matrix.

Simulation experiments confirm the theoretical properties.

Applications show improved portfolio and macroeconomic data predictions.

Abstract

We consider the estimation of a sparse factor model where the factor loading matrix is assumed sparse. The estimation problem is reformulated as a penalized M-estimation criterion, while the restrictions for identifying the factor loading matrix accommodate a wide range of sparsity patterns. We prove the sparsistency property of the penalized estimator when the number of parameters is diverging, that is the consistency of the estimator and the recovery of the true zeros entries. These theoretical results are illustrated by finite-sample simulation experiments, and the relevance of the proposed method is assessed by applications to portfolio allocation and macroeconomic data prediction.