Block-diagonal idiosyncratic covariance estimation in high-dimensional factor models for financial time series

TL;DR

This paper introduces a new method for estimating the idiosyncratic covariance matrix in high-dimensional factor models, using clustering and shrinkage to improve accuracy and positive definiteness in financial data analysis.

Contribution

The paper proposes a novel block-diagonal covariance estimator based on clustering residuals, outperforming existing thresholding methods in simulations and real data.

Findings

The proposed estimators reliably estimate the idiosyncratic covariance.

They outperform state-of-the-art thresholding methods in accuracy.

The methods ensure positive definiteness of the estimated matrices.

Abstract

Estimation of high-dimensional covariance matrices in latent factor models is an important topic in many fields and especially in finance. Since the number of financial assets grows while the estimation window length remains of limited size, the often used sample estimator yields noisy estimates which are not even positive definite. Under the assumption of latent factor models, the covariance matrix is decomposed into a common low-rank component and a full-rank idiosyncratic component. In this paper we focus on the estimation of the idiosyncratic component, under the assumption of a grouped structure of the time series, which may arise due to specific factors such as industries, asset classes or countries. We propose a generalized methodology for estimation of the block-diagonal idiosyncratic component by clustering the residual series and applying shrinkage to the obtained blocks in order to ensure positive definiteness. We derive two different estimators based on different clustering methods and test their performance using simulation and historical data. The proposed methods are shown to provide reliable estimates and outperform other state-of-the-art estimators based on thresholding methods.