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Estimation of a Multiplicative Covariance Structure

Authors: Christian M. Hafner , Oliver Linton and Haihan Tang
Date: 17 May 2016
Type: cemmap Working Paper, CWP23/16
DOI: 10.1920/wp.cem.2016.2316

Abstract

We consider a Kronecker product structure for large covariance matrices, which has the feature that the number of free parameters increases logarithmically with the dimensions of the matrix. We propose an estimation method of the free parameters based on the log linear property of this structure, and also a Quasi-Likelihood method. We establish the rate of convergence of the estimated parameters when the size of the matrix diverges. We also establish a CLT for our method. We apply the method to portfolio choice for S&P500 daily returns and compare with sample covariance based methods and with the recent Fan et al. (2013) method.

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Christian M. Hafner, Oliver Linton and Haihan Tang November 2016, Estimation of a multiplicative covariance structure in the large dimensional case, cemmap Working Paper, CWP52/16, The IFS

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