Estimation of a Multiplicative Correlation Structure in the Large Dimensional Case

Christian Hafner, Oliver Linton and Haihan Tang

Cambridge Working Papers in Economics from Faculty of Economics, University of Cambridge

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.

Keywords: Correlation matrix; Kronecker product; Matrix logarithm; Multiway; array data; Portfolio choice; Sparsity (search for similar items in EconPapers)
JEL-codes: C55 C58 G11 (search for similar items in EconPapers)
Date: 2018-09-28
New Economics Papers: this item is included in nep-ecm and nep-ore
Note: obl20
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Related works:
Journal Article: Estimation of a multiplicative correlation structure in the large dimensional case (2020)
Working Paper: Estimation of a multiplicative correlation structure in the large dimensional case (2020)
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Persistent link: https://EconPapers.repec.org/RePEc:cam:camdae:1878

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