The main objective of the thesis was to investigate the feasibility of accurately and precisely fore- casting the number of both national and provincial bene ciaries of social security grants in South Africa, using simple autoregressive integrated moving average (ARIMA) models. The series of the monthly number of bene ciaries of the old age, child support, foster care and disability grants from April 2004 to March 2010 were used to achieve the objectives of the thesis. The conclusions from analysing the series were that: (1) ARIMA models for forecasting are province and grant-type spe- ci c; (2) for some grants, national forecasts obtained by aggregating provincial ARIMA forecasts are more accurate and precise than those obtained by ARIMA modelling national series; and (3) for some grants, forecasts obtained by modelling the latest half of the series were more accurate and precise than those obtained from modelling the full series. / Mathematical Sciences / M.Sc. (Statistics)

Thesis (MBA (Business Management))--University of Stellenbosch, 2008. / ENGLISH ABSTRACT: To date, there has been significant research completed on the topic of corporate financial distress. Two pioneering researchers in the field of predicting financial distress was Beaver in 1966 and Altman in 1968. More recent research, based on companies listed on the JSE has been that of Steyn-Bruwer and Hamman (2006). This project, based on the latter authors’ work, has been formulated with one main research objective and two subordinate research objectives. The main research objective is to prove that different modelling techniques provide better prediction accuracies than others. The two subordinate research objectives are firstly to prove that there is a difference in the overall predictive accuracy if the data (provided by Steyn-Bruwer and Hamman) is subdivided according to “year before failure” and not according to economic period and secondly to prove that more optimised, independent variables would provide a better overall predictive accuracy. This research report summarises several significant papers on the topic; and draws the conclusion that research on financial distress is fragmented with very little consensus on any of the major definitions, assumptions and findings. In order to contextualise these differences; this research report defines and discusses corporate financial distress and considers the major issues associated with the field of research. An interesting observation from the literature survey was the fact that existing literature does not readily take consideration of the number of Type I and Type II errors made. As such, this research report introduces a novel concept (not seen in other research) called the “Normalised Cost of Failure” (NCF) which takes cognisance of the fact that a Type I error typically costs 20 to 38 times that of a Type II error. In order to satisfy the main research objective several different modelling techniques were selected based on their popularity in the literature surveyed. They are: Multiple Discriminant Analysis (MDA), Recursive Partitioning (RP), Logit Analysis (LA) and Neural Networks (NN). A summary of each of the different techniques is provided in Chapter 4 of this research report. The research by Steyn-Bruwer and Hamman forms the departure point for this research and their work is summarised in Chapter 5 of this report. Chapters 6, 7 and 8 use the data from Steyn-Bruwer and Hamman along with the above mentioned modelling techniques to verify the main and subordinate objectives. In terms of the main research objective, the results of these chapters show that the different analysis techniques definitely produce different predictive accuracies. Here, the MDA and RP techniques correctly predict the most “failed” companies; and consequently have the lowest NCF. This research report also shows that LA and NN provide the best overall predictive accuracy. In terms of the first subordinate research objective; this research shows that using the year before failure rather than the economic period as a subdivision provides superior predictive accuracy. With regard to the second subordinate research objective: there is no difference in the predictive accuracies if the independent variables are further optimised. These results were disappointing and consequently disprove the second subordinate objective that widening the number of input variables actually improves the predictive accuracy. In fact, the results indicate that the information contained in the independent variables seems to saturate after the most important (key predictor) independent variables have been included in the model. It is important to take cognisance of the fact that each predictive technique has its own strength and weakness. It is proposed by the author that the strengths and weaknesses of these predictive techniques be combined to provide a better overall predictive methodology. / AFRIKAANSE OPSOMMING: Heelwat betekenisvolle navorsing oor die onderwerp van maatskappye se finansiële verknorsing is tot op hede voltooi. Twee baanbreker-navorsers op die gebied van vooruitskatting van finansiële verknorsing was Beaver in 1966 en Altman in 1968. Meer onlangse navorsing, gebaseer op maatskappye wat op die JSE genoteer is, was dié van Steyn-Bruwer en Hamman (2006). Hierdie navorsingsverslag, gebaseer op die voorgenoemde outeurs se werk, is geformuleer met een hoofnavorsingsdoelwit en twee ondergeskikte navorsingsdoelwitte. Die hoofnavorsingsdoelwit is om te bewys dat verskillende modelleringstegnieke beter voorspellingsakkuraatheid as andere het. Die twee ondergeskikte navorsingsdoelwitte is, eerstens, dat daar ʼn verskil is in die oorhoofse voorspellingsakkuraatheid as die data (verskaf deur Steyn-Bruwer en Hamman) onderverdeel word volgens die “jaar voor mislukking” eerder as volgens die ekonomiese tydperk; en tweedens, om te bewys dat meer geoptimiseerde, onafhanklike veranderlikes kan lei tot ʼn beter oorhoofse voorspellingsakkuraatheid. Ten einde hierdie verskille te konseptualiseer, het hierdie navorsingsverslag finansiële mislukkings van maatskappye bespreek en gedefinieer en aandag geskenk aan die belangrikste aspekte geassosieer met die navorsingsveld. ʼn Interessante waarneming uit die literatuurstudie was die feit dat die huidige literatuur selde indien enige, oorweging skenk aan die aantal Tipe I- en Tipe II-foute wat gemaak word. As sulks het hierdie navorsingsprojek ʼn nuwe begrip (nog nie in ander navorsing gesien nie) ontwikkel, wat beskryf word as die “Genormaliseerde Kostefaktor”; wat die feit dat ʼn Tipe I-fout tipies 20 tot 38 maal die koste van ʼn Tipe II-fout beloop, in ag neem. Ten einde te voldoen aan die hoofnavorsingsdoelwit is verskillende modelleringstegnieke wat op grond van hul gewildheid in die literatuur voorgekom het, gekies. Hulle is: Meervoudige Diskriminantanalise (MDA), Herhalende Verdeling (RP), Logit-Analise (LA) en Neurale Netwerke (NN). ʼn Opsomming van elk van hierdie verskillende tegnieke word in Hoofstuk 4 van hierdie navorsingsverslag verskaf. Die navorsing wat deur Steyn-Bruwer en Hamman gedoen is, vorm die vertrekpunt van hierdie navorsing en hulle werk is gevolglik in Hoofstuk 5 van hierdie verslag opgesom. Hoofstukke 6, 7 en 8 gebruik die data van Steyn-Bruwer en Hamman tesame met die bovermelde modelleringstegnieke ten einde die hoof- en ondergeskikte doelwitte te bewys. In terme van die hoofnavorsingsdoelwit, het die resultate van hierdie hoofstukke getoon dat die verskillende analitiese tegnieke definitief verskillende voorspellingsakkuraatheid oplewer. Hier het die MDA- en RP-tegnieke die grootste aantal mislukte maatskappye korrek voorspel, en gevolglik die laagste Genormaliseerde Kostefaktor gehad. Die navorsingsverslag toon ook dat LA en NN die beste oorhoofse akkuraatheid van voorspelling het. In terme van die eerste ondergeskikte navorsingsprobleem het hierdie navorsing getoon dat, om die jaar voor mislukking te gebruik as onderverdeling, eerder as die ekonomiese tydperk, beter voorspellingsakkuraatheid het. Wat die tweede ondergeskikte navorsingsdoelwit betref, is daar bevind dat daar geen verskille in die voorspellingsakkuraatheid bestaan as die individuele veranderlikes verder geoptimaliseer word nie. Hierdie resultate was teleurstellend en het gevolglik die tweede ondergeskikte probleem, naamlik dat as die aantal inset-veranderlikes sou vergroot word, dit die vooruitskattingsakkuraatheid behoort te kan verhoog, verkeerd bewys. Tewens, die resultate het getoon dat die inligting soos vervat in die onafhanklike veranderlikes klaarblyklik versadiging bereik nadat die belangrikste (hoof-vooruitskatter) onafhanklike veranderlikes in die model opgeneem is. Dit is belangrik om kennis te neem van die feit dat elke vooruitskattingstegniek sy eie sterk en swak punte het. Die skrywer stel dus voor dat hierdie sterk- en swakpunte gekombineerd gebruik word om ʼn beter oorhoofse vooruitskattingsmetodologie daar te stel.

Abstracts in English, Afrikaans and Northern Sotho / More time series forecasting methods were researched and made available in recent years. This is mainly due to the emergence of machine learning methods which also found applicability in time series forecasting. The emergence of a variety of methods and their variants presents a challenge when choosing appropriate forecasting methods. This study explored the performance of four advanced forecasting methods: autoregressive integrated moving averages (ARIMA); artificial neural networks (ANN); support vector machines (SVM) and regression models with ARIMA errors. To improve their performance, bagging was also applied. The performance of the different methods was illustrated using South African air passenger data collected for planning purposes by the Airports Company South Africa (ACSA). The dissertation discussed the different forecasting methods at length. Characteristics such as strengths and weaknesses and the applicability of the methods were explored. Some of the most popular forecast accuracy measures were discussed in order to understand how they could be used in the performance evaluation of the methods. It was found that the regression model with ARIMA errors outperformed all the other methods, followed by the ARIMA model. These findings are in line with the general findings in the literature. The ANN method is prone to overfitting and this was evident from the results of the training and the test data sets. The bagged models showed mixed results with marginal improvement on some of the methods for some performance measures. It could be concluded that the traditional statistical forecasting methods (ARIMA and the regression model with ARIMA errors) performed better than the machine learning methods (ANN and SVM) on this data set, based on the measures of accuracy used. This calls for more research regarding the applicability of the machine learning methods to time series forecasting which will assist in understanding and improving their performance against the traditional statistical methods / Die afgelope tyd is verskeie tydreeksvooruitskattingsmetodes ondersoek as gevolg van die ontwikkeling van masjienleermetodes met toepassings in die vooruitskatting van tydreekse. Die nuwe metodes en hulle variante laat ʼn groot keuse tussen vooruitskattingsmetodes. Hierdie studie ondersoek die werkverrigting van vier gevorderde vooruitskattingsmetodes: outoregressiewe, geïntegreerde bewegende gemiddeldes (ARIMA), kunsmatige neurale netwerke (ANN), steunvektormasjiene (SVM) en regressiemodelle met ARIMA-foute. Skoenlussaamvoeging is gebruik om die prestasie van die metodes te verbeter. Die prestasie van die vier metodes is vergelyk deur hulle toe te pas op Suid-Afrikaanse lugpassasiersdata wat deur die Suid-Afrikaanse Lughawensmaatskappy (ACSA) vir beplanning ingesamel is. Hierdie verhandeling beskryf die verskillende vooruitskattingsmetodes omvattend. Sowel die positiewe as die negatiewe eienskappe en die toepasbaarheid van die metodes is uitgelig. Bekende prestasiemaatstawwe is ondersoek om die prestasie van die metodes te evalueer. Die regressiemodel met ARIMA-foute en die ARIMA-model het die beste van die vier metodes gevaar. Hierdie bevinding strook met dié in die literatuur. Dat die ANN-metode na oormatige passing neig, is deur die resultate van die opleidings- en toetsdatastelle bevestig. Die skoenlussamevoegingsmodelle het gemengde resultate opgelewer en in sommige prestasiemaatstawwe vir party metodes marginaal verbeter. Op grond van die waardes van die prestasiemaatstawwe wat in hierdie studie gebruik is, kan die gevolgtrekking gemaak word dat die tradisionele statistiese vooruitskattingsmetodes (ARIMA en regressie met ARIMA-foute) op die gekose datastel beter as die masjienleermetodes (ANN en SVM) presteer het. Dit dui op die behoefte aan verdere navorsing oor die toepaslikheid van tydreeksvooruitskatting met masjienleermetodes om hul prestasie vergeleke met dié van die tradisionele metodes te verbeter. / Go nyakišišitšwe ka ga mekgwa ye mentši ya go akanya ka ga molokoloko wa dinako le go dirwa gore e hwetšagale mo mengwageng ye e sa tšwago go feta. Se k e k a le b a k a la g o t šwelela ga mekgwa ya go ithuta ya go diriša metšhene yeo le yona e ilego ya dirišwa ka kakanyong ya molokolokong wa dinako. Go t šwelela ga mehutahuta ya mekgwa le go fapafapana ga yona go tšweletša tlhohlo ge go kgethwa mekgwa ya maleba ya go akanya. Dinyakišišo tše di lekodišišitše go šoma ga mekgwa ye mene ya go akanya yeo e gatetšego pele e lego: ditekanyotshepelo tšeo di kopantšwego tša poelomorago ya maitirišo (ARIMA); dinetweke tša maitirelo tša nyurale (ANN); metšhene ya bekthara ya thekgo (SVM); le mekgwa ya poelomorago yeo e nago le diphošo tša ARIMA. Go kaonafatša go šoma ga yona, nepagalo ya go ithuta ka metšhene le yona e dirišitšwe. Go šoma ga mekgwa ye e fepafapanego go laeditšwe ka go šomiša tshedimošo ya banamedi ba difofane ba Afrika Borwa yeo e kgobokeditšwego mabakeng a dipeakanyo ke Khamphani ya Maemafofane ya Afrika Borwa (ACSA). Sengwalwanyaki šišo se ahlaahlile mekgwa ya kakanyo ye e fapafapanego ka bophara. Dipharologanyi tša go swana le maatla le bofokodi le go dirišega ga mekgwa di ile tša šomišwa. Magato a mangwe ao a tumilego kudu a kakanyo ye e nepagetšego a ile a ahlaahlwa ka nepo ya go kwešiša ka fao a ka šomišwago ka gona ka tshekatshekong ya go šoma ga mekgwa ye. Go hweditšwe gore mokgwa wa poelomorago wa go ba le diphošo tša ARIMA o phadile mekgwa ye mengwe ka moka, gwa latela mokgwa wa ARIMA. Dikutollo tše di sepelelana le dikutollo ka kakaretšo ka dingwaleng. Mo k gwa wa ANN o ka fela o fetišiša gomme se se bonagetše go dipoelo tša tlhahlo le dihlo pha t ša teko ya tshedimošo. Mekgwa ya nepagalo ya go ithuta ka metšhene e bontšhitše dipoelo tšeo di hlakantšwego tšeo di nago le kaonafalo ye kgolo go ye mengwe mekgwa ya go ela go phethagatšwa ga mešomo. Go ka phethwa ka gore mekgwa ya setlwaedi ya go akanya dipalopalo (ARIMA le mokgwa wa poelomorago wa go ba le diphošo tša ARIMA) e šomile bokaone go phala mekgwa ya go ithuta ka metšhene (ANN le SVM) ka mo go sehlopha se sa tshedimošo, go eya ka magato a nepagalo ya magato ao a šomišitšwego. Se se nyaka gore go dirwe dinyakišišo tše dingwe mabapi le go dirišega ga mekgwa ya go ithuta ka metšhene mabapi le go akanya molokoloko wa dinako, e lego seo se tlago thuša go kwešiša le go kaonafatša go šoma ga yona kgahlanong le mekgwa ya setlwaedi ya dipalopalo. / Decision Sciences / M. Sc. (Operations Research)