HIGH DIMENSIONAL COVARIANCE MATRIX ESTIMATION IN APPROXIMATE FACTOR MODELS

By Jianqing Fan, Yuan Liao, Martina Mincheva. Annals of Statistics, 2011

417 citations recorded by the source corpus.

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 (2011), 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.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5d3a2c38d5c4ae3f19afc5891cc230b9afbc74f0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. D. Xiu
2. Jianqing Fan
3. Yacine Aït-Sahalia
4. Clifford Lam
5. Kunpeng Li
6. Yuan Liao
7. Jushan Bai
8. Tommaso Cai

In Statistics and Probability

1. Jianqing Fan
2. Yuan Liao
3. Tommaso Cai
4. Clifford Lam
5. Jushan Bai
6. D. Xiu
7. Zhao Ren
8. Harrison H. Zhou

Citations in the corpus

• Large Covariance Estimation by Thresholding Principal Orthogonal Complements (2011, neutral): “The conditional sparsity structure of (1.2) was explored by Fan, Liao and Mincheva (2011) in estimating the covariance matrix, when the factors {ft} are observable.”
• NETS: Network estimation for time series (2019, neutral): “The model captures an important fraction of total variability, on top of what is explained by volatility factors, and improves out-of-sample forecasting.”
• PROJECTED PRINCIPAL COMPONENT ANALYSIS IN FACTOR MODELS (2014, background): “2); Fan et al. (2012). The separations between the common factors and idiosyncratic components are carried out by the low-rank plus sparsity decomposition. See, for example, Candes and Recht (2009); Fan et al. (2011); Koltchinskii et al. (2011); Negahban and Wainwright (2011); Fan et al. (2013); Cai”
• Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (2016, background): “Under other similar assumptions as those in Fan et al. (2011), the rates of convergence cn,p (log p/n) 1/2 for estimating Σ−1U and Σ −1 under the spectral norm are derived, assuming ΣU ∈ H0(cn,p).”
• Statistical inference for principal components of spiked covariance matrices (2020, background): “[33] J.”
• A Trace-restricted Kronecker-Factored Approximation to Natural Gradient (2020, neutral): “…in many fields and there have been many new methodological approaches to covariance estimation in the large dimensional case (i.e., the dimension of the covariance matrix is large compared with the sample size) (Ledoit and Wolf, 2004; Fan and Mincheva, 2011; Hoff, 2016; Linton and Tang, 2019).”
• Using Principal Component Analysis to Estimate a High Dimensional Factor Model with High-Frequency Data (2017, methodology): “In a setting with low-frequency time series data, Fan et al. (2011) and Fan et al. (2013) suggest imposing the sparsity assumption on the residual covariance matrix.”
• Modeling and Forecasting Large Realized Covariance Matrices and Portfolio Choice (2017, neutral): “Several other papers have dealt with the estimation of vast covariance matrices, e.g. Bickel and Levina (2008), Levina et al. (2008), Fan et al. (2008), Wang and Zou (2010), Fan et al. (2011), Fan et al. (2012), Fan et al. (2012), Hautsch et al. (2012), Fan et al. (2013).”
• Feasible generalized least squares for panel data with cross-sectional and serial correlations (2019, methodology): “Both Friedberg (1998) and Wolfers (2006) used a weighted model by muliplying all variables by the square root of state population.”
• A Nodewise Regression Approach to Estimating Large Portfolios (2016, methodology): “The performance of these models was documented by Fan, Liao, and Mincheva (2011) and Fan, Liao, and Mincheva (2013).”
• Estimation and Inference of FAVAR Models (2014, methodology): “Large dimensional factor models are also increasingly used outside macroeconomics and finance, for example, Fan, Liao, and Mincheva (2011), Fan, Liao and Mincheva (2013), and Tsai and Tsay (2010).)”
• Maximum Likelihood Estimation and Inference for Approximate Factor Models of High Dimension (2016, methodology): “The Arbitrage Pricing Theory (APT) of Ross (1976), for example, is built upon a multiple factor model for asset returns.”