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Hafner, C., Linton, O., Tang, H.

Estimation of a Multiplicative Correlation Structure in the Large Dimensional Case


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

JEL Codes: C55 C58 G11

Author links: Oliver Linton  


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