Factor Models with Real Data: a Robust Estimation of the Number of Factors

TL;DR

This paper addresses the challenge of robustly estimating the number of factors in high-dimensional data models when the covariance matrix must be estimated from data, proposing strategies to handle uncertainty in practical scenarios.

Contribution

It introduces a new method for robustly estimating the number of factors in factor models considering the uncertainty in covariance matrix estimation from real data.

Findings

Proposes a strategy for robust factor number estimation

Addresses issues arising from covariance matrix estimation errors

Improves accuracy of factor model descriptions in practical data analysis

Abstract

Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in mathematical terms as follows. We are given the covariance matrix Sigma of the available data. Sigma must be additively decomposed as the sum of two positive semidefinite matrices D and L: D | that accounts for the idiosyncratic noise affecting the knowledge of each component of the available vector of data | must be diagonal and L must have the smallest possible rank in order to describe the available data in terms of the smallest possible number of independent factors. In practice, however, the matrix Sigma is never known and therefore it must be estimated from the data so that only an approximation of Sigma is actually available. This paper discusses the issues that arise from this uncertainty and provides a strategy to deal with the problem of robustly estimating the number of factors.