Estimation of a Multiplicative Covariance Structure in the Large Dimensional Case

Christian M. Hafner and Oliver Linton

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

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-identification. 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.

Keywords: Correlation Matrix; Kronecker Product; Matrix Logarithm; Multiarray data; Multi-trai Multi method; Portfolio Choice; Sparsity (search for similar items in EconPapers)
Date: 2016-11-09
New Economics Papers: this item is included in nep-ecm
Note: obl20
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Related works:
Working Paper: Estimation of a multiplicative covariance structure in the large dimensional case (2016)
Working Paper: Estimation of a Multiplicative Covariance Structure in the Large Dimensional Case (2016)
Working Paper: Estimation of a multiplicative covariance structure in the large dimensional case (2016)
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Persistent link: https://EconPapers.repec.org/RePEc:cam:camdae:1664

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