{"id":1612,"date":"2021-04-13T11:52:00","date_gmt":"2021-04-13T10:52:00","guid":{"rendered":"http:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/?p=1612"},"modified":"2022-11-11T10:24:53","modified_gmt":"2022-11-11T10:24:53","slug":"analysing-the-distribution-of-garch-innovations-dr-kirstin-strokorb","status":"publish","type":"post","link":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/analysing-the-distribution-of-garch-innovations-dr-kirstin-strokorb\/","title":{"rendered":"Analysing the distribution of GARCH innovations &#8211; Supervisor:  Dr. Kirstin Strokorb"},"content":{"rendered":"<p style=\"color: #383735\"><strong>Title of project:<\/strong><br \/>\nAnalysing the distribution of GARCH innovations<\/p>\n<p style=\"color: #383735\"><strong>Code:<\/strong><br \/>\nKS2122A<\/p>\n<p style=\"color: #383735\"><strong>Supervisor:\u00a0<\/strong><br \/>\nDr. Kirstin Strokorb<\/p>\n<p><strong>Project description:<\/strong><br \/>\nWhen modelling \ufb01nancial time series with GARCH(1,1) processes, the distribution of the GARCH innovations plays a key role in dynamic risk managment. For instance, choosing either Student-t innovations or normal innovations as a modelling approach can lead to over- or underestimation of potential risks. The literature often suggests that Student-t innovations seem to be more appropriate in most practically relevant situations. However, it has also been noted that, even when we simulate a GARCH time series with normally distributed innovations and re-estimate the innovations using standard MLE methods, the re-estimated innovations typically resemble more a Student-t sample rather than a normal one. This indicates that standard methods are typically not robust and can lead to misspeci\ufb01cation. Sun and Zhou (2014) develop a statistical test that is based on analysing \u201dimplied tail indices\u201d in order to make it easier to distinguish between Student-t and normal innovations.<\/p>\n<p><strong>Guiding questions:<\/strong><br \/>\nThe aim of this project is to understand the main reasoning of this testing procedure, to implement it using statistical software, to study its performance and robustness in simulated scenarios and \ufb01nally, to analyse the innovations of some real \ufb01nancial time series using the Sun and Zhou (2014) procedure.<\/p>\n<p><strong>Main literature suggestion (starting point):<\/strong><br \/>\n\u2022 P. Sun and C. Zhou (2014). Diagnosing the distribution of GARCH innovations. Journal of Empirical Finance, 29, 287-303.<br \/>\n\u2022 conceivably references therein as needed<\/p>\n<p style=\"color: #383735\"><strong>Project offered as double module, single module, or both:<\/strong><br \/>\nSingle<\/p>\n<p style=\"color: #383735\"><strong>Prerequisite Modules:<\/strong><br \/>\nFoundations of Probability and Statistics (MA2500)<br \/>\nEconometrics for Financial Mathematics (MA2801)<br \/>\nProgramming and Statistics (MA2501)<\/p>\n<p style=\"color: #383735\"><strong>Number of students who could be supervised for this project:<\/strong><br \/>\n1<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Title of project: Analysing the distribution of GARCH innovations Code: KS2122A Supervisor:\u00a0 Dr. Kirstin Strokorb Project description: When modelling \ufb01nancial time series with GARCH(1,1) processes, the distribution of the GARCH innovations plays a key role in dynamic risk managment. For instance, choosing either Student-t innovations or normal innovations as a modelling approach can lead to &hellip; <a href=\"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/analysing-the-distribution-of-garch-innovations-dr-kirstin-strokorb\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Analysing the distribution of GARCH innovations &#8211; Supervisor:  Dr. Kirstin Strokorb<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[2,5,7],"tags":[],"class_list":["post-1612","post","type-post","status-publish","format-standard","hentry","category-2021-2022","category-single","category-yr-3-descriptions-2021-2022"],"aioseo_notices":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts\/1612","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/comments?post=1612"}],"version-history":[{"count":6,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts\/1612\/revisions"}],"predecessor-version":[{"id":1895,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/posts\/1612\/revisions\/1895"}],"wp:attachment":[{"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/media?parent=1612"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/categories?post=1612"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.maths.cf.ac.uk\/mathsugprojects\/wp-json\/wp\/v2\/tags?post=1612"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}