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An application of copulas to improve PCA biplots for multivariate extremes
Thesis (MCom)--Stellenbosch University, 2018.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2018
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| _version_ | 1867614002943623168 |
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| access_status_str | Open Access |
| author | Perrang, Justin |
| author2 | Van der Merwe, Carel Johannes |
| author_browse | Perrang, Justin Van der Merwe, Carel Johannes |
| author_facet | Van der Merwe, Carel Johannes Perrang, Justin |
| author_sort | Perrang, Justin |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MCom)--Stellenbosch University, 2018. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/104861 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:45:06.534Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2018 |
| publishDateRange | 2018 |
| publishDateSort | 2018 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/104861 An application of copulas to improve PCA biplots for multivariate extremes Perrang, Justin Van der Merwe, Carel Johannes Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science. Principal components analysis Biplots Copulas (Mathematical statistics) Financial data -- Statistical methods Extreme value theory UCTD Thesis (MCom)--Stellenbosch University, 2018. ENGLISH SUMMARY : Principal Component Analysis (PCA) biplots is a valuable means of visualising high dimensional data. The application of PCA biplots over a wide variety of research areas containing multivariate data is well documented. However, the application of biplots to financial data is limited. This is partly due to PCA being an inadequate means of dimension reduction for multivariate data that is subject to extremes. This implies that its application to financial data is greatly diminished since extreme observations are common in financial data. Hence, the purpose of this research is to develop a method to accommodate PCA biplots for multivariate data containing extreme observations. This is achieved by fitting an elliptical copula to the data and deriving a correlation matrix from the copula parameters. The copula parameters are estimated from only extreme observations and as such the derived correlationmatrices contain the dependencies of extreme observations. Finally, applying PCA to such an “extremal” correlation matrix more efficiently preserves the relationships underlying the extremes and a more refined PCA biplot can be constructed. AFRIKAANSE OPSOMMING : Hoofkomponent Analise (HKA) bistippings is ’n nuttige metode ommeer dimensionele data te visualiseer. Die toepassing van HKA bistippings is al goed gedokumenteer oor ’n wye verskeidenheid van navorsingsareas waar meerveranderlike data voorkom, maar die toepassing van bistippings op finansiële data is beperk. Dit is deels te wyte aan HKA wat ‘n onvoldoende metode is van dimensie reduksie van meerveranderlike data wat ekstreme waarnemings bevat. Dit impliseer dat die toepassing daarvan op finansiële data aansienlik beperk is, gegee dat ekstreme waarnemings algemeen voorkom in finansiële data. Die doel van hierdie navorsing is om ’n metode te ontwikkel om HKA- bistippings toe te pas op meerveranderlike data wat ekstreme waarnemings bevat. Dit word gedoen deur ’n elliptiese copula op die data te pas en ‘n korrelasiematriks uit die copula parameters af te lei. Die copula parameters word beraam deur slegs die ekstreme waarnemings te gebruik en dus dui die afgeleide korrelasiematrikse die afhanklikhede van slegs ekstreme waarnemings aan. Laastens, deur HKA op so ’n “ekstreme” korrelasie matriks toe te pas, word die verwantskappe onderliggend aan die ekstreme waardes meer doeltreffend behou en kan ’n meer onderskeidende HKA bistipping gekonstrueer word. Masters 2018-11-05T11:14:19Z 2018-12-07T06:48:07Z 2018-11-05T11:14:19Z 2018-12-07T06:48:07Z 2018-12 Thesis http://hdl.handle.net/10019.1/104861 en_ZA Stellenbosch University 125 pages ; illustrations, includes annexures application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Principal components analysis Biplots Copulas (Mathematical statistics) Financial data -- Statistical methods Extreme value theory UCTD Perrang, Justin An application of copulas to improve PCA biplots for multivariate extremes |
| title | An application of copulas to improve PCA biplots for multivariate extremes |
| title_full | An application of copulas to improve PCA biplots for multivariate extremes |
| title_fullStr | An application of copulas to improve PCA biplots for multivariate extremes |
| title_full_unstemmed | An application of copulas to improve PCA biplots for multivariate extremes |
| title_short | An application of copulas to improve PCA biplots for multivariate extremes |
| title_sort | application of copulas to improve pca biplots for multivariate extremes |
| topic | Principal components analysis Biplots Copulas (Mathematical statistics) Financial data -- Statistical methods Extreme value theory UCTD |
| url | http://hdl.handle.net/10019.1/104861 |
| work_keys_str_mv | AT perrangjustin anapplicationofcopulastoimprovepcabiplotsformultivariateextremes AT perrangjustin applicationofcopulastoimprovepcabiplotsformultivariateextremes |