Tests for Group-Specific Heterogeneity in High-Dimensional Factor Models

TL;DR

This paper introduces two new statistical tests to detect group-specific heterogeneity in high-dimensional factor models, which are useful for understanding distinct cyclical behaviors across variable groups in economics and finance.

Contribution

The paper develops novel tests for identifying heterogeneity in factor loadings across groups, with theoretical validation and practical permutation-based implementation.

Findings

Tests effectively detect heterogeneity in simulations

Permutation approach accurately approximates distributions

Empirical application reveals group-specific effects in financial data

Abstract

Standard high-dimensional factor models assume that the comovements in a large set of variables could be modeled using a small number of latent factors that affect all variables. In many relevant applications in economics and finance, heterogenous comovements specific to some known groups of variables naturally arise, and reflect distinct cyclical movements within those groups. This paper develops two new statistical tests that can be used to investigate whether there is evidence supporting group-specific heterogeneity in the data. The first test statistic is designed for the alternative hypothesis of group-specific heterogeneity appearing in at least one pair of groups; the second is for the alternative of group-specific heterogeneity appearing in all pairs of groups. We show that the second moment of factor loadings changes across groups when heterogeneity is present, and use this feature to establish the theoretical validity of the tests. We also propose and prove the validity of a permutation approach for approximating the asymptotic distributions of the two test statistics. The simulations and the empirical financial application indicate that the proposed tests are useful for detecting group-specific heterogeneity.