https://ir.unisa.ac.za/handle/10500/2788 2026-05-12T21:08:22Z https://ir.unisa.ac.za/handle/10500/29805 On fractional volatility modelling Mpanda, Marc Mukendi In this thesis, we investigate the roughness feature within realised volatility for different financial markets by using the multifractal detrended fluctuation approach and microstructure noise index technique, and we confirm that the Hurst parameter H 6= 1/2. To include this feature in stochastic volatility modelling, we construct an arbitrage-free financial market model that con sists of two assets, the risk-free and the risky assets. The price of a risk-free asset is described by an exponential function while the one for a risky as set is driven by a geometric Brownian motion with its stochastic volatility described as a function of fractional Cox-Ingersoll-Ross process defined by Yt = Z 2 t , where the process (Zt)t≥0 satisfies a singular stochastic differential driven by fractional Brownian motion (WH t )t≥0, H∈(0,1). The stochastic pro cess (Zt)t≥0 verifies dZt = 2022-08-01T00:00:00Z https://ir.unisa.ac.za/handle/10500/29281 Performance improvements in machine learning approaches for fault detection and soft sensing in the process industry Mazibuko, Tshidiso The main focus of this research is on the application of machine learning in solving problems that have not been solved by the advancement in process simulation and automation tools in the process industry. These problems are the fault detection and diagnosis, and soft sensing of variables that are difficult and/or expensive to measure. A literature review was conducted in areas where the application of machine learning was used to solve the problems related to fault detection and diagnosis, and soft sensing of process variables. Two case studies from the literature review were further extended, with the aim of improving the performance of the machine learning approaches to these problems. The first case study is on the detection of process faults for the Tennessee Eastman chemical process. In this case study, unsupervised sequential data-driven models such as the long short-term memory autoencoder (LSTM autoencoder), dynamic autoencoder and the dynamic principal component analysis (PCA) are explored. The results show that the LSTM and the dynamic autoencoder improved the detection of five faults that were poorly detected in the original case study by at least 60%. The second case study is the optimisation of a steam boiler control system using machine learning. In this case study, the contribution made is the use of feature selection in improving the performance of the machine learning models used in predicting the temperature of six zones in the boiler (to minimise overheating of tubes) and the oxygen content on both sides of the flue system (to maximise combustion efficiency). The results show that feature selection decreased the mean squared error (MSE) and mean absolute percentage error (MAPE) by 60% and 50% respectively. 2021-12-01T00:00:00Z https://ir.unisa.ac.za/handle/10500/27410 Exploring advanced forecasting methods with applications in aviation Riba, Evans Mogolo 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. Abstracts in English, Afrikaans and Northern Sotho 2021-02-01T00:00:00Z https://ir.unisa.ac.za/handle/10500/27343 The complexity of unavoidable word patterns Sauer, Paul Van der Merwe The avoidability, or unavoidability of patterns in words over finite alphabets has been studied extensively. The word α over a finite set A is said to be unavoidable for an infinite set B+ of nonempty words over a finite set B if, for all but finitely many elements w of B+, there exists a semigroup morphism φ ∶ A+ → B+ such that φ(α) is a factor of w. In this treatise, we start by presenting a historical background of results that are related to unavoidability. We present and discuss the most important theorems surrounding unavoidability in detail. We present various complexity-related properties of unavoidable words. For words that are unavoidable, we provide a constructive upper bound to the lengths of words that avoid them. In particular, for a pattern α of length n over an alphabet of size r, we give a concrete function N(n, r) such that no word of length N(n, r) over the alphabet of size r avoids α. A natural subsequent question is how many unavoidable words there are. We show that the fraction of words that are unavoidable drops exponentially fast in the length of the word. This allows us to calculate an upper bound on the number of unavoidable patterns for any given finite alphabet. Subsequently, we investigate computational aspects of unavoidable words. In particular, we exhibit concrete algorithms for determining whether a word is unavoidable. We also prove results on the computational complexity of the problem of determining whether a given word is unavoidable. Specifically, the NP-completeness of the aforementioned problem is established. Bibliography: pages 192-195 2019-12-01T00:00:00Z