Estimation of a multiplicative correlation structure in the large dimensional case
(2020) Journal of Econometrics — Vol. 217, n° 2, p. 431-470 (2020)
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- Abstract
- (en) 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.
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Hafner, C., Linton, O., & Tang, H. (2020). Estimation of a multiplicative correlation structure in the large dimensional case. Journal of Econometrics, 217(2), 431-470. https://doi.org/10.1016/j.jeconom.2019.12.012 (Original work published 2020)