matrices-correlation-invalid - Collection of invalid correlation matrices

About

matrices-correlation-invalid is a collection of MATLAB functions that generate invalid correlation matrices: matrices that are intended to be correlation matrices but for various reasons relating to their construction have a negative eigenvalue and so are not positive semidefinite. The matrices are taken from the literature and from applications. They are used in

N. J. Higham and N. Strabić, "Bounds for the Distance to the Nearest Correlation Matrix", SIAM J. Matrix Anal. Appl., 37(3): 1088-1102, 2016,

and

N. J. Higham and N. Strabić, "Anderson Acceleration of the Alternating Projections Method for Computing the Nearest Correlation Matrix", Numer. Algorithms, 72(4):1021-1042, 2016.

The matrices are

• bccd16: 3250-by-3250 matrix from EU bank data.

• beyu11: 12-by-12 matrix based on tetrachoric estimates.

• bhwi01: 5-by-5 matrix relating to portfolio risk.

• cor1399: 1399-by-1399 matrix constructed from stock data.

• cor3120: 3120-by-3120 matrix constructed from stock data.

• fing97: 7-by-7 matrix from stress testing.

• high02: 3-by-3 matrix.

• mmb13: 6-by-6 matrix from foreign exchange trading data supplied by the Royal Bank of Scotland.

• tec03: 4-by-4 matrix from stress testing.

• tyda99r1, tyda99r2, and tyda99r3: 8-by-8 matrices from resource allocation modeling.

• usgs13: 94-by-94 matrix from national assessment of carbon dioxide storage resources in the USA.

Other M-files:

• test_run: test function that generates the matrices and prints the dimension and smallest eigenvalue of each matrix. Run this to make sure that the collection is properly installed.

• treshape: a utility function for converting vectors to triangular matrices and vice versa. This is taken from the Matrix Computation Toolbox.

• am_properties.m: lists properties of the matrices and is intended for use when this collection is integrated as a group in the Anymatrix collection.

Anymatrix Integration

This collection is ready to include as a group in the Anymatrix collection, for which the command

anymatrix('g','corrinv','higham/matrices-correlation-invalid')

should be used, which gives the group the name corrinv.

Requirements

The codes have been developed under MATLAB 2015b and 2016a.

License

See license.txt for licensing information.