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Quantitative Finance · Glossary

What is Nearest correlation matrix?

Definition 23.11 Quantitative Methods · Chapter 23 — Convex Optimisation

The nearest correlation matrix to a symmetric matrix CC is the positive semidefinite matrix with unit diagonal closest to CC in the Frobenius norm, a semidefinite programme that Higham (2002) solves by alternating projections with Dykstra’s correction.

Eigenvalues (in increasing order; the largest, above 10, off the chart) of a pairwise-complete correlation matrix of fifty series with half the data missing, and of its nearest correlation matrix. Twenty-one negative eigenvalues become zero. Data: the chapter’s tutorial, seeded.
Figure 23.3. Eigenvalues (in increasing order; the largest, above 10, off the chart) of a pairwise-complete correlation matrix of fifty series with half the data missing, and of its nearest correlation matrix. Twenty-one negative eigenvalues become zero. Data: the chapter’s tutorial, seeded.
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