Nonparametric Estimation of Large Covariance Matrices with Conditional Sparsity

58 Pages Posted: 30 Jan 2020

See all articles by Hanchao Wang

Hanchao Wang

Zhejiang University - College of Economics; Shandong University - Zhongtai Securities Institute for Financial Studies

Bin Peng

Deakin University - Faculty of Business and Law

Degui Li

University of York

Chenlei Leng

University of Warwick - Department of Statistics

Date Written: January 6, 2020

Abstract

This paper studies estimation of covariance matrices with conditional sparse structure. We overcome the challenge of estimating dense matrices using a factor structure, the challenge of estimating large-dimensional matrices by postulating sparsity on the covariance of the random noises, and the challenge of estimating varying matrices by allowing factor loadings to smoothly change. A kernel-weighted estimation approach combined with generalised shrinkage is proposed. Under mild conditions, we derive uniform consistency for the developed estimation method and obtain convergence rates. Numerical studies including simulation and an empirical application are presented to examine the finite-sample performance of the developed methodology.

Keywords: Approximate Factor Model, Kernel Estimation, Large Covariance Matrix, Sparsity, Uniform Convergence

JEL Classification: C13, C23, G11

Suggested Citation

Wang, Hanchao and Peng, Bin and Li, Degui and Leng, Chenlei, Nonparametric Estimation of Large Covariance Matrices with Conditional Sparsity (January 6, 2020). Available at SSRN: https://ssrn.com/abstract=3515624 or http://dx.doi.org/10.2139/ssrn.3515624

Hanchao Wang

Zhejiang University - College of Economics ( email )

Yuquan Campus 38 Zheda Road
Hangzhou, Zhejiang 310027
China

Shandong University - Zhongtai Securities Institute for Financial Studies ( email )

27 Shanda South Road
Jinan City, Shandong 250100
China

Bin Peng

Deakin University - Faculty of Business and Law ( email )

Burwood, Victoria 3215
Australia

Degui Li (Contact Author)

University of York ( email )

Deparment of Mathematics
University of York
Heslington, York YO10 5DD
United Kingdom

Chenlei Leng

University of Warwick - Department of Statistics ( email )

Coventry, CV47AL
United Kingdom

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