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Analysing GARCH models across different sample sizes
Thesis (MCom)--Stellenbosch University, 2023.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2023
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| _version_ | 1867613948438642688 |
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| access_status_str | Open Access |
| author | Purchase, Michael Andrew |
| author2 | Conradie, Willie |
| author_browse | Conradie, Willie Purchase, Michael Andrew |
| author_facet | Conradie, Willie Purchase, Michael Andrew |
| author_sort | Purchase, Michael Andrew |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Thesis (MCom)--Stellenbosch University, 2023. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/127220 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:44:15.221Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2023 |
| publishDateRange | 2023 |
| publishDateSort | 2023 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/127220 Analysing GARCH models across different sample sizes Purchase, Michael Andrew Conradie, Willie Viljoen, Helena Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science. GARCH model Econometrics Distribution (Probability theory) UCTD Thesis (MCom)--Stellenbosch University, 2023. ENGLISH SUMMARY: As initially constructed by Robert Engle and his student Tim Bollerslev, the GARCH model has the desired ability to model the changing variance (heteroskedasticity) of a time series. The primary goal of this study is to investigate changes in volatility, estimates of the parameters, forecasting error as well as excess kurtosis across different window lengths as this may indicate an appropriate sample size to use when fitting a GARCH model to a set of data. After examining the T = 6489 1-day logreturns on the FTSE/JSE-ALSI between 27 December 1995 and 15 December 2021, it was calculated that an average estimate for volatility of 0.193 670 should be expected. Given that a rolling window methodology was applied across 20 different window lengths under both the S-GARCH(1,1) and E-GARCH(1,1) models, a total of 180 000 GARCH models were fit with parameter and volatility estimates, information criteria and volatility forecasts being extracted. Given the construction of the asymmetric response function under the E-GARCH model, this model has greater ability to account for the `leverage effect' where negative market returns are greater drivers of higher volatility than positive returns of an equal magnitude. Among others, key results include volatility estimates across most window lengths taking longer to settle after the Global Financial Crisis (GFC) than after the COVID-19 pandemic. This was interesting because volatility reached higher levels during the latter, indicating that the South African market reacted more severely to the COVID-19 pandemic but also managed to adjust to new market conditions quicker than those after the Global Financial Crisis. In terms of parameter estimates under the S-GARCH(1,1) model, values for a and b under a window length of 100 trading days were often calculated infinitely close to zero and one respectively, indicating a strong possibility of the optimising algorithm arriving at local maxima of the likelihood function. With the exceptionally low p-values under the Jarque-Bera and Kolmogorov-Smirnov tests as well as all excess kurtosis values being greater than zero, substantial motivation was provided for the use of the Student's t-distribution when fitting GARCH models. Given the various results obtained around volatility, parameter estimates, RMSE and information criteria, it was concluded that a window length of 600 is perhaps the most appropriate when modelling GARCH volatility. AFRIKAANSE OPSOMMING: Die GARCH-model, oorspronklik ontwikkel deur Robert Engle en Tim Bollerslev, besit die gewenste eienskap dat dit die veranderende variansie (heteroskedastisiteit) van 'n tydreeks kan modelleer. Die primere doel van hierdie studie is om veranderinge in volatiliteit, die beramings van die parameters, voorspellingsfoute, sowel as oortollige kurtose oor verskillende vensterperiodes te ondersoek, aangesien dit tot 'n toepaslike steekproefgrootte kan lei wat gebruik kan word wanneer 'n GARCH-model op 'n stel data toegepas word. Nadat die T = 6489 1-dag log-opbrengs op die FTSE/JSE-ALSI tussen 27 Desember 1995 en 15 Desember 2021 ondersoek is, is daar gevind dat 'n gemiddelde beraming vir volatiliteit van 0.193 670 verwag kan word. Gegewe dat 'n rolvenster-metodologie toegepas is oor 20 verskillende vensterperiodes vir beide die S-GARCH(1,1)- en E-GARCH(1,1)- modelle, is 'n totaal van 180 000 GARCH-modelle met parameter- en volatiliteitskattings gepas, met inligtingskriteria en volatiliteitsvoorspellings wat onttrek is. Gegewe die konstruksie van die asimmetriese responsfunksie onder die E-GARCH-model, het hierdie model 'n beter vermoe om rekening te hou met die `hefboome_ek' waar negatiewe markopbrengste groter drywers van hoer volatiliteit is as positiewe opbrengste van 'n dieselfde grootte. Sleutelresultate sluit onder meer volatiliteitsberamings oor die meeste vensterperiodes in, wat langer neem om te stabiliseer na die Globale Finansielekrisis (GFC) as na die COVID-19-pandemie. Dit was interessant omdat volatiliteit tydens die laasgenoemde tydperk hoer vlakke bereik het, wat daarop dui dat die Suid-Afrikaanse mark erger op die COVID-19-pandemie gereageer het, maar ook daarin geslaag het om vinniger by nuwe marktoestande aan te pas as na die GFC. In terme van parameterberamings onder die S-GARCH(1,1)-model, is waardes gevind vir _ en _ onder 'n vensterperiode van 100 handelsdae wat dikwels oneindig naby aan nul en een is, onderskeidelik, wat sterk daarop dui dat die optimaliseringsalgoritme lokale maksimums van die waarskynlikheidsfunksie bereik. Met die buitengewoon lae p-waardes onder die Jarque-Bera- en Kolmogorov-Smirnov-toetse, sowel as alle oormaat kurtosewaardes wat groter as nul is, is aansienlike motivering verskaf vir die gebruik van die Student se t-verdeling wanneer GARCH-modelle gepas word. Gegewe die verskillende resultate wat verkry is rondom volatiliteit, parameterberamings, RMSE en inligtingskriteria, is tot die gevolgtrekking gekom dat 'n vensterperiode van 600 moontlik die geskikste is wanneer GARCH-volatiliteit gemodelleer word. Masters 2023-03-04T15:01:07Z 2023-05-18T07:10:28Z 2023-03-04T15:01:07Z 2023-05-18T07:10:28Z 2023-03 Thesis http://hdl.handle.net/10019.1/127220 en_ZA Stellenbosch University xv, 93 pages : illustrations, includes annexures application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | GARCH model Econometrics Distribution (Probability theory) UCTD Purchase, Michael Andrew Analysing GARCH models across different sample sizes |
| title | Analysing GARCH models across different sample sizes |
| title_full | Analysing GARCH models across different sample sizes |
| title_fullStr | Analysing GARCH models across different sample sizes |
| title_full_unstemmed | Analysing GARCH models across different sample sizes |
| title_short | Analysing GARCH models across different sample sizes |
| title_sort | analysing garch models across different sample sizes |
| topic | GARCH model Econometrics Distribution (Probability theory) UCTD |
| url | http://hdl.handle.net/10019.1/127220 |
| work_keys_str_mv | AT purchasemichaelandrew analysinggarchmodelsacrossdifferentsamplesizes |