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

ArXiv ID: 2407.03781 “View on arXiv”

Authors: Unknown

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.

Keywords: Covariance matrix estimation, Latent factor models, Idiosyncratic component, Shrinkage estimation, Clustering, Equities

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper features dense mathematical formulations including latent factor models, eigenvalue analysis, and derivations of estimators, indicating high math complexity. It also demonstrates strong empirical rigor through comprehensive simulations, historical data backtests, out-of-sample portfolio performance evaluation, and comparisons with state-of-the-art methods.

  flowchart TD
    A["Research Goal<br>Estimate block-diagonal idiosyncratic<br>covariance in high-dim factor models"] --> B["Input Data<br>High-dimensional asset returns<br>Finite time windows"]
    B --> C{"Key Methodology Steps"}
    C --> D["Cluster residuals<br>Identify structure<br>(e.g., industries/assets)"]
    D --> E["Apply Shrinkage<br>Within clustered blocks<br>Ensure positive definiteness"]
    E --> F["Computational Process<br>Simulate data / Historical backtesting<br>vs. Thresholding estimators"]
    F --> G["Key Findings/Outcomes<br>Reliable covariance estimates<br>Outperforms state-of-the-art methods<br>Handles limited sample size"]