High-dimensional covariance matrix estimation in approximate factor models

Abstract

The variance--covariance matrix plays a central role in the inferential theories of high-dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu [J. Amer. Statist. Assoc. 106 (2011) 672--684], taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high dimensionality on the covariance matrix estimation based on the factor structure is then studied.

Published in at http://dx.doi.org/10.1214/11-AOS944 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Regularized estimation of large covariance matrices
• Covariance regularization by thresholding
• Sparsistency and rates of convergence in large covariance matrix estimation
• A Bernstein type inequality and moderate deviations for weakly dependent sequences

Cited by in corpus (64)

• Simultaneous multiple change-point and factor analysis for high-dimensional time series
• Distributed ARIMA Models for Ultra-long Time Series
• Gaussian and bootstrap approximations for high-dimensional U-statistics and their applications
• Posterior contraction in sparse Bayesian factor models for massive covariance matrices
• Stable Estimation of a Covariance Matrix Guided by Nuclear Norm Penalties
• A Hybrid Framework for Topology Identification of Distribution Grid with Renewables Integration
• Rank Determination in Tensor Factor Model
• Feasible Generalized Least Squares for Panel Data with Cross-sectional and Serial Correlations
• Large Covariance Estimation through Elliptical Factor Models
• Multi-Scale Factor Analysis of High-Dimensional Brain Signals
• Escaping the curse of dimensionality in Bayesian model based clustering
• KoPA: Automated Kronecker Product Approximation
• Factor Models for Matrix-Valued High-Dimensional Time Series
• Tensor Factor Model Estimation by Iterative Projection
• A large covariance matrix estimator under intermediate spikiness regimes
• When and why are principal component scores a good tool for visualizing high-dimensional data?
• Random matrix approach to estimation of high-dimensional factor models
• Estimation of functionals of sparse covariance matrices
• Robust high dimensional factor models with applications to statistical machine learning
• An Overview on the Estimation of Large Covariance and Precision Matrices
• Hypothesis testing for eigenspaces of covariance matrix
• A Projection Based Conditional Dependence Measure with Applications to High-dimensional Undirected Graphical Models
• Interpolating Predictors in High-Dimensional Factor Regression
• Deep Risk Model: A Deep Learning Solution for Mining Latent Risk Factors to Improve Covariance Matrix Estimation
• Performance of Empirical Risk Minimization for Linear Regression with Dependent Data
• Batch greedy maximization of non-submodular functions: Guarantees and applications to experimental design
• De-biased graphical Lasso for high-frequency data
• Estimation of False Discovery Proportion with Unknown Dependence
• Optimal Covariance Estimation for Condition Number Loss in the Spiked Model
• Volume Weighted Average Price Optimal Execution
• A two-way factor model for high-dimensional matrix data
• Gaussian approximation for the sup-norm of high-dimensional matrix-variate U-statistics and its applications
• Penalized Sparse Covariance Regression with High Dimensional Covariates
• On the benefits of index insurance in US agriculture: a large-scale analysis using satellite data
• Estimation of the Kronecker Covariance Model by Quadratic Form
• Sparse Approximate Factor Estimation for High-Dimensional Covariance Matrices
• Block-diagonal idiosyncratic covariance estimation in high-dimensional factor models for financial time series
• Covariate Assisted Variable Ranking
• Dual subgradient algorithms for large-scale nonsmooth learning problems
• A Factor-Adjusted Multiple Testing Procedure with Application to Mutual Fund Selection
• Power Enhancement in High Dimensional Cross-Sectional Tests
• Estimation for ultra-high dimensional factor model: a pivotal variable detection based approach
• Testing for Conditional Mean Independence with Covariates through Martingale Difference Divergence
• Optimal estimation of functionals of high-dimensional mean and covariance matrix
• Detecting approximate replicate components of a high-dimensional random vector with latent structure
• How well can we learn large factor models without assuming strong factors?
• Network-Assisted Estimation for Large-dimensional Factor Model with Guaranteed Convergence Rate Improvement
• Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data
• A Trace-restricted Kronecker-Factored Approximation to Natural Gradient
• Bayesian Regularization for Graphical Models with Unequal Shrinkage
• Bootstrapping ${\ell }_p$-Statistics in High Dimensions
• Adaptive Reference-Guided Estimation of Principal Component Subspace in High Dimensions
• AR-sieve Bootstrap for High-dimensional Time Series
• Robust Inference of Risks of Large Portfolios
• Pre-processing with Orthogonal Decompositions for High-dimensional Explanatory Variables
• Large Volatility Matrix Prediction with High-Frequency Data
• Factor Models for High-Dimensional Functional Time Series
• Mixed-normal limit theorems for multiple Skorohod integrals in high-dimensions, with application to realized covariance
• High-dimensional covariance matrix estimation using a low-rank and diagonal decomposition
• Factor-augmented Smoothing Model for Functional Data
• Combining Smoothing Spline with Conditional Gaussian Graphical Model for Density and Graph Estimation
• Diagonally-Dominant Principal Component Analysis
• A Dynamic Structure for High Dimensional Covariance Matrices and its Application in Portfolio Allocation
• Learning from Forecast Errors: A New Approach to Forecast Combinations