Characterizing Correlation Matrices that Admit a Clustered Factor Representation

TL;DR

This paper investigates the structure of correlation matrices that can be represented by a clustered factor model, revealing limitations of the traditional approach and proposing a new parametrization to overcome these restrictions.

Contribution

The paper characterizes correlation matrices compatible with the CF model and introduces a novel parametrization using logarithmic transformation to relax superfluous restrictions.

Findings

CF model imposes unnecessary restrictions on correlation matrices

Logarithmic transformation of block correlation matrices offers a more flexible parametrization

New parametrization broadens the class of correlation matrices representable by the CF model

Abstract

The Clustered Factor (CF) model induces a block structure on the correlation matrix and is commonly used to parameterize correlation matrices. Our results reveal that the CF model imposes superfluous restrictions on the correlation matrix. This can be avoided by a different parametrization, involving the logarithmic transformation of the block correlation matrix.