Estimation of a multiplicative correlation structure in the large dimensional case

Christian Hafner, Oliver Linton and Haihan Tang
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Haihan Tang: Fudan University

No 2020028, LIDAM Reprints ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: We propose a Kronecker product model for correlation or covariance matrices in the large dimensional 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 rates of convergence and central limit theorems (CLT) for our estimators in the large dimensional case. A specification test and tools for Kronecker product model selection and inference are provided. In a 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 (search for similar items in EconPapers)
JEL-codes: C55 C58 G11 (search for similar items in EconPapers)
Date: 2020-01-01
Note: In: Journal of Econometrics - Vol. 217, no.2, p. 431-470 (2020)
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Citations: View citations in EconPapers (4)

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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 (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvar:2020028

DOI: 10.1016/j.jeconom.2019.12.012

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