Testing for sparse idiosyncratic components in factor-augmented regression models

TL;DR

This paper introduces a bootstrap test to detect sparse idiosyncratic components in factor regression models, demonstrating high power in simulations and applications to macroeconomic and financial data.

Contribution

The paper develops a novel bootstrap testing procedure for identifying sparsity in factor-augmented regression models, with proven asymptotic properties and a data-driven tuning parameter selection method.

Findings

High power against sparse alternatives in simulations

Often reject the null in macroeconomic and finance datasets

Supports presence of sparsity beyond dense models in economic data

Abstract

We propose a novel bootstrap test of a dense model, namely factor regression, against a sparse plus dense alternative augmenting model with sparse idiosyncratic components. The asymptotic properties of the test are established under time series dependence and polynomial tails. We outline a data-driven rule to select the tuning parameter and prove its theoretical validity. In simulation experiments, our procedure exhibits high power against sparse alternatives and low power against dense deviations from the null. Moreover, we apply our test to various datasets in macroeconomics and finance and often reject the null. This suggests the presence of sparsity -- on top of a dense model -- in commonly studied economic applications. The R package FAS implements our approach.