centre for microdata methods and practice

ESRC centre

cemmap is an ESRC research centre

ESRC

Keep in touch

Subscribe to cemmap news

Estimation of a multiplicative covariance structure in the large dimensional case

Authors: Christian M. Hafner , Oliver Linton and Haihan Tang
Date: 09 November 2016
Type: cemmap Working Paper, CWP52/16
DOI: 10.1920/wp.cem.2016.5216

Abstract

We propose a Kronecker product structure for large covariance or correlation matrices. One feature of this model is that it scales logarithmically with dimension in the sense that the number of free parameters increases logarithmically with the dimension of the matrix. We propose an estimation method of the parameters based on a log-linear property of the structure, and also a quasi-maximum likelihood estimation (QMLE) method. We establish the rate of convergence of the estimated parameters when the size of the matrix diverges. We also establish a central limit theorem (CLT) for our method. We derive the asymptotic distributions of the estimators of the parameters of the spectral distribution of the Kronecker product correlation matrix, of the extreme logarithmic eigenvalues of this matrix, and of the variance of the minimum variance portfolio formed using this matrix. We also develop tools of inference including a test for over-identifi cation. We apply our methods to portfolio choice for S&P500 daily returns and compare with sample covariance-based methods and with the recent Fan, Liao, and Mincheva (2013) method.

Download full version
Previous version:
Christian M. Hafner, Oliver Linton and Haihan Tang May 2016, Estimation of a Multiplicative Covariance Structure, cemmap Working Paper, CWP23/16, IFS

Publications feeds

Subscribe to cemmap working papers via RSS

Search cemmap

Search by title, topic or name.

Contact cemmap

Centre for Microdata Methods and Practice

How to find us

Tel: +44 (0)20 7291 4800

E-mail us