A majorization algorithm for constrained correlation matrix approximation

Linear Algebra and Its Applications

Volumn 432, Issue 5, 2010, Pages 1152-1164

  Simon, Dan ^a   Abell, Jeff ^b  

^a Cleveland State University   (United States)

^b GENERAL MOTORS CORPORATION   (United States)

Author keywords

Constrained optimization; Correlation matrix; Majorization

Indexed keywords

APPROXIMATION ERRORS; COMPUTATIONAL EFFORT; CORRELATION MATRIX; FROBENIUS NORM; INPUT MATRICES; MAJORIZATION; OPTIMALITY CRITERIA; SPECIFIC PROBLEMS;

APPROXIMATION ALGORITHMS; CORRELATION METHODS;

CONSTRAINED OPTIMIZATION;

EID: 72049121663     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2009.10.025     Document Type: Article

References (30)

1. Al-Subaihi A. Simulating correlated multivariate pseudorandom numbers. J. Statist. Software 9 4 (2004).
2. M. Anjos, N. Higham, P. Takouda, H. Wolkowicz, A semidefinite programming approach for the nearest correlation matrix problem, Optimization Online, September 16, 2003. .
3. Apolinario J., and Diniz P. A new fast QR algorithm based on a priori errors. IEEE Signal Process. Lett. 4 11 (1997) 307-309
4. Bernstein D. Matrix Mathematics (2005), Princeton University Press
5. Borg I., and Groenen P. Modern Multidimensional Scaling (1997), Springer
6. Brigo D., and Mercurio F. Interest Rate Models - Theory and Practice (2006), Springer
7. Brigo D., and Mercurio F. Calibrating LIBOR. Risk Mag. 15 1 (2002) 117-122
8. C. Brooks, B. Scott-Quinn, J. Walmsley, Adjusting VAR models for the impact of the EURO, July 20, 1998.
9. Budden M., Hadavas P., Hoffman L., and Pretz C. Generating valid 4 × 4 correlation matrices. Appl. Math. E-Notes 7 (2007) 53-59
10. Cohen L. Quality Function Deployment (1995), Springer
11. Dash J. Quantitative Finance and Risk Management (2004), World Scientific
12. J. de Leeuw, A decomposition method for weighted least squares low-rank approximation of symmetric matrices, UCLA Department of Statistics Paper 2006041602, April 16, 2006. .
13. Flury B. Common Principal Components and Related Multivariate Models (1988), John Wiley & Sons
14. I. Grubisic, Interest Rate Theory: The BGM Model, Masters Thesis, Leiden University, August 2002. .
15. Grubisic I., and Pietersz R. Efficient rank reduction of correlation matrices. Linear Algebra Appl. 422 2-3 (2007) 629-653
16. Higham N. Matrix nearness problems and applications. In: Gover M., and Barnett S. (Eds). Applications of Matrix Theory (1989), Clarendon Press 1-27
17. Higham N. Computing the nearest correlation matrix - A problem from finance. IMA J. Numer. Anal. 22 3 (2002) 329-343
18. Hoge W. A subspace identification extension to the phase correlation method. IEEE Trans. Med. Imaging 22 2 (2003) 277-280
19. Kenneth Crow and Associates, Refrigerator Product Planning Matrix, 2007. .
20. Kourti T. Process analysis and abnormal situation detection: from theory to practice. IEEE Control Syst. Mag. 22 5 (2002) 10-25
21. S. Mishra, Optimal solution of the nearest correlation matrix problem by minimization of the maximum norm, Social Sci. Res. Network, August 6, 2004. .
22. S. Mishra, Completing correlation matrices of arbitrary order by differential evolution method of global optimization: a Fortran program, Social Sci. Res. Network, March 5, 2007. SSRN: .
23. S. Mishra, The nearest correlation matrix problem: solution by differential evolution method of global optimization, Research Papers in Economics, April 14, 2007. .
24. Moon T., and Stirling W. Mathematical Methods and Algorithms for Signal Processing (2000), Prentice-Hall
25. Morini M., and Webber N. An EZI method to reduce the rank of a correlation matrix in financial modelling. Appl. Math. Finance 13 4 (2006) 309-331
26. Pietersz R., and Groenen P. Rank reduction of correlation matrices by majorization. Quant. Finance 4 6 (2004) 649-662
27. H. Qi, D. Sun, Correlation stress testing for value-at-risk: an unconstrained convex optimization approach, March 2007. .
28. Rebonato R., and Jackel P. The most general methodology to create a valid correlation matrix for risk management and option pricing purposes. J. Risk 2 2 (1999) 17-27
29. Simon D. Reduced order Kalman filtering without model reduction. Control Intell. Syst. 35 2 (2007) 169-174
30. Zhang Z., and Wu L. Optimal low-rank approximation to a correlation matrix. Linear Algebra Appl. 364 (2003) 161-187