Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/189785 
Year of Publication: 
2016
Series/Report no.: 
cemmap working paper No. CWP52/16
Publisher: 
Centre for Microdata Methods and Practice (cemmap), London
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.
Subjects: 
Correlation Matrix
Kronecker Product
Matrix Logarithm
Multiarray data
Multi-trai Multi method
Portfolio Choice
Sparsity
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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