Repository logo
 

Estimation of a Multiplicative Correlation Structure in the Large Dimensional Case


Type

Working Paper

Change log

Authors

Hafner, C. 
Linton, O. 
Tang, H. 

Abstract

We propose a Kronecker product model for correlation or covariance matrices in the large dimension case. The number of parameters of the model increases logarithmically with the dimension of the matrix. We propose a minimum distance (MD) estimator based on a log-linear property of the model, as well as a one-step estimator, which is a one-step approximation to the quasi-maximum likelihood estimator (QMLE).We establish the rate of convergence and a central limit theorem (CLT) for our estimators in the large dimensional case. A specification test and tools for Kronecker product model selection and inference are provided. In an Monte Carlo study where a Kronecker product model is correctly specified, our estimators exhibit superior performance. In an empirical application to portfolio choice for S&P500 daily returns, we demonstrate that certain Kronecker product models are good approximations to the general covariance matrix.

Description

Keywords

Correlation matrix, Kronecker product, Matrix logarithm, Multiway, array data, Portfolio choice, Sparsity

Is Part Of

Publisher

Faculty of Economics

Publisher DOI

Publisher URL