Computing Nearest Covariance and Correlation Matrices

Lucas, Craig (2001) Computing Nearest Covariance and Correlation Matrices. Masters thesis, Manchester Institute for Mathematical Sciences, The University of Manchester.

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Abstract

We look at two matrix nearness problems posed by a finance company, where nearness is measured in the Frobenius norm. Correlation and covariance matrices are computed from sampled stock data with missing entries by a technique that produces matrices that are not positive semidefinite. In the first problem we find the nearest correlation matrix that is positive semidefinite and preserves any correlations known to be exact. In the second problem we investigate how the missing elements in the data should be chosen in order to generate the nearest covariance matrix to the indefinite matrix from the completed set of data. We show how the former problem can be solved using an alternating projections algorithm and how the latter problem can be investigated using a multi-directional search optimization method.

Item Type: Thesis (Masters)
Uncontrolled Keywords: nearest positive semidefinite correlation covariance matrices
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User: Dr Craig Lucas
Date Deposited: 11 Jun 2015
Last Modified: 20 Oct 2017 14:13
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2311

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