Computing Nearest Covariance and Correlation Matrices
Craig Lucas · MIMS EPrints (University of Southampton) · 2001
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.