Computing the Nearest Correlation Matrix - a Problem From Finance (2002) [15 citations — 0 self]
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author = {Nicholas J. Higham},
title = {Computing the Nearest Correlation Matrix - a Problem From Finance},
year = {2002}
}
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Abstract:
Introduction A correlation matrix is a symmetric positive semidefinite matrix with unit diagonal. Correlation matrices occur in several areas of numerical linear algebra, including preconditioning of linear systems and error analysis of Jacobi methods for the symmetric eigenvalue problem (see Davies & Higham (2000) for details and references). The term `correlation matrix' comes from statistics, since a matrix whose (i, j ) entry is the correlation coefficient between two random variables x i and x j is symmetric positive semidefinite with unit diagonal. It is a statistical application that motivates this work---one coming from the finance industry. In stock research sample correlation matrices constructed from vectors of stock returns are used for predictive purposes. Unfortunately, on any day when an observation is made data are rarely available for all the stocks of interest. One way to deal with this problem is to compute the sample correlations of pairs of stocks using data draw
