Computing Nearest Correlation Matrix via Low-Rank ODE’s Based Technique
For <i>n</i>-dimensional real-valued matrix <i>A</i>, the computation of nearest correlation matrix; that is, a symmetric, positive semi-definite, unit diagonal and off-diagonal entries between <inline-formula><math display="inline"><semantics><...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
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Multidisciplinary Digital Publishing Institute
2021
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| Online Access: | https://hdl.handle.net/1721.1/131319 |
| _version_ | 1826202374479282176 |
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| author | Rehman, Mutti-Ur Alzabut, Jehad Abodayeh, Kamaleldin |
| author2 | Massachusetts Institute of Technology. Department of Chemical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Chemical Engineering Rehman, Mutti-Ur Alzabut, Jehad Abodayeh, Kamaleldin |
| author_sort | Rehman, Mutti-Ur |
| collection | MIT |
| description | For <i>n</i>-dimensional real-valued matrix <i>A</i>, the computation of nearest correlation matrix; that is, a symmetric, positive semi-definite, unit diagonal and off-diagonal entries between <inline-formula><math display="inline"><semantics><mrow><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula> and 1 is a problem that arises in the finance industry where the correlations exist between the stocks. The proposed methodology presented in this article computes the admissible perturbation matrix and a perturbation level to shift the negative spectrum of perturbed matrix to become non-negative or strictly positive. The solution to optimization problems constructs a gradient system of ordinary differential equations that turn over the desired perturbation matrix. Numerical testing provides enough evidence for the shifting of the negative spectrum and the computation of nearest correlation matrix. |
| first_indexed | 2024-09-23T12:06:27Z |
| format | Article |
| id | mit-1721.1/131319 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T12:06:27Z |
| publishDate | 2021 |
| publisher | Multidisciplinary Digital Publishing Institute |
| record_format | dspace |
| spelling | mit-1721.1/1313192023-02-22T17:21:32Z Computing Nearest Correlation Matrix via Low-Rank ODE’s Based Technique Rehman, Mutti-Ur Alzabut, Jehad Abodayeh, Kamaleldin Massachusetts Institute of Technology. Department of Chemical Engineering For <i>n</i>-dimensional real-valued matrix <i>A</i>, the computation of nearest correlation matrix; that is, a symmetric, positive semi-definite, unit diagonal and off-diagonal entries between <inline-formula><math display="inline"><semantics><mrow><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula> and 1 is a problem that arises in the finance industry where the correlations exist between the stocks. The proposed methodology presented in this article computes the admissible perturbation matrix and a perturbation level to shift the negative spectrum of perturbed matrix to become non-negative or strictly positive. The solution to optimization problems constructs a gradient system of ordinary differential equations that turn over the desired perturbation matrix. Numerical testing provides enough evidence for the shifting of the negative spectrum and the computation of nearest correlation matrix. 2021-09-20T14:16:11Z 2021-09-20T14:16:11Z 2020-11-04 2020-11-12T14:13:50Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/131319 Symmetry 12 (11): 1824 (2020) PUBLISHER_CC http://dx.doi.org/10.3390/sym12111824 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ application/pdf Multidisciplinary Digital Publishing Institute Multidisciplinary Digital Publishing Institute |
| spellingShingle | Rehman, Mutti-Ur Alzabut, Jehad Abodayeh, Kamaleldin Computing Nearest Correlation Matrix via Low-Rank ODE’s Based Technique |
| title | Computing Nearest Correlation Matrix via Low-Rank ODE’s Based Technique |
| title_full | Computing Nearest Correlation Matrix via Low-Rank ODE’s Based Technique |
| title_fullStr | Computing Nearest Correlation Matrix via Low-Rank ODE’s Based Technique |
| title_full_unstemmed | Computing Nearest Correlation Matrix via Low-Rank ODE’s Based Technique |
| title_short | Computing Nearest Correlation Matrix via Low-Rank ODE’s Based Technique |
| title_sort | computing nearest correlation matrix via low rank ode s based technique |
| url | https://hdl.handle.net/1721.1/131319 |
| work_keys_str_mv | AT rehmanmuttiur computingnearestcorrelationmatrixvialowrankodesbasedtechnique AT alzabutjehad computingnearestcorrelationmatrixvialowrankodesbasedtechnique AT abodayehkamaleldin computingnearestcorrelationmatrixvialowrankodesbasedtechnique |