Accelerometer data can be analyzed using a variety of methods which are effective in the clinical setting. Time-series analysis is used to analyze spatiotemporal variables in various populations. More recently, investigators have focused on gait complexity and the structure of spatiotemporal variations during walking and running. This study evaluated the use of time-series analyses to determine gait parameters during running. Subjects were college-age female soccer players. Accelerometer data were collected using GPS-embedded trunk-mounted accelerometers. Customized Matlab® programs were developed that included Gaussian continuous wavelet transform (CWT) to determine spatiotemporal characteristics, detrended fluctuation analysis (DFA) to examine gait complexity and autocorrelation analyses (ACF) to assess gait regularity. Reliability was examined using repeated running efforts and intraclass correlation. Proof of concept was determined by examining differences in each variable between various running speeds. Applicability was established by examining gait before and after fatiguing activity. The results showed most variables had excellent reliability. Test-retest R2 values for these variables ranged from 0.8 to 1.0. Low reliability was seen in bilateral comparisons of gait symmetry. Increases in running speed resulted in expected changes in spatiotemporal and acceleration variables. Fatiguing exercise had minimal effects on spatiotemporal variables but resulted in noticeable declines in complexity. This investigation shows that GPS-embedded trunk-mounted accelerometers can be effectively used to assess running gait. CWT and DFA yield reliable measures of spatiotemporal characteristics of gait and gait complexity. The effects of running speed and fatigue on these variables provides proof of concepts and applicability for this analytical approach. / Master of Science / Fitness trackers have become widely accessible and easy to use. So much so that athletic teams have been using them to track activity throughout the season. Researchers are able to manipulate data generated from the fitness monitors to assess many different variables including gait. Monitoring gait may generate important information about the condition of the individual. As a person fatigues, running form is theorized to breakdown, which increases injury risk. Therefore the ability to monitor gait may be advantageous in preventing injury. The purpose of this study is to show that the methods in this study are reproducible, respond reasonably to changes in speed, and to observe the changes of gait in the presence of fatigue or on tired legs. Three analyses are used in this study. The first method called autocorrelation, overlays acceleration signals of consecutive foot strikes, and determines the similarity between them. The second method utilizes a wave transformation technique that is able to determine foot contact times. The final method attempts to determine any pattern in the running stride. This method looks for changes in the structure of the pattern. Less structure would indicate a stride that is fatigued. The results showed that the methods of gait analysis used in this study were reproducible and responded appropriately with changes in speed. Small changes in gait were observed due to the presence of fatigue. Further investigation into the use of these methods to determine changes in gait due to the presence of fatigue are warranted.

The rapid evolution of Connected and Autonomous Vehicles (CAVs) has led to a surge in research on efficient anomaly detection methods to ensure their safe and reliable operation. While state-of-the-art deep learning models offer promising results in this domain, their high computational requirements present challenges for deployment in resource-constrained environments, such as Electronic Control Units (ECU) in vehicles. In this context, we consider using the ensemble learning technique specifically the cascaded modeling approach for real-time and resource-efficient multivariate time series anomaly detection in CAVs. The study was done in collaboration with SCANIA, a transport solutions provider. The company is now undergoing a transformation of providing autonomous and sustainable solutions and this work will contribute towards that transformation. Our methodology employs unsupervised learning techniques to construct a cascade of models, comprising a coarse-grained model with lower computational complexity at level one, and a more intricate fine-grained model at level two. Furthermore, we incorporate cascaded model training to refine the complex model's ability to make decisions on uncertain and anomalous events, leveraging insights from the simpler model. Through extensive experimentation, we investigate the trade-off between model performance and computational complexity, demonstrating that our proposed cascaded model achieves greater efficiency with no performance degradation. Further, we do a comparative analysis of the impact of probabilistic versus deterministic approaches and assess the feasibility of model training at edge environments using the Federated Learning concept.

Komplexe Netzwerke sind mächtige Werkzeuge, die die Untersuchung komplexer Systeme unterstützen. In vielen Bereichen werden komplexe Netzwerke eingesetzt, um die Dynamik interagierender Entitäten wie Neuronen, Menschen oder sogar Wettersysteme zu verstehen. Darüber hinaus erweitern sich die Anwendungsbereiche mit der stetigen Entwicklung neuer theoretischer Ansätze. In dieser Arbeit wollen wir sowohl den theoretischen Rahmen der Netzwerkwissenschaften weiterentwickeln als auch komplexe Netzwerke in der Klimatologie und der computergestützten Sozialwissenschaft anwenden. / Complex networks are powerful tools enabling the study of complex systems. In many fields, complex networks are used as a tool to gain an understanding of the dynamics of interacting entities such as neurons in a brain, humans on social media, or global weather systems. At the same time, new theoretical frameworks that extend the toolbox of Network Science promote the application of network tools in new research fields. In this thesis, we aim for both, advancing the theoretical framework of Network Science as well as applying complex networks in Climatology and Computational Social Science.

Die Modellierung komplexer Systeme mit einer großen Anzahl von Freiheitsgraden ist in den letzten Jahrzehnten zu einer großen Herausforderung geworden. In der Regel werden nur einige wenige Variablen komplexer Systeme in Form von gemessenen Zeitreihen beobachtet, während die meisten von ihnen - die möglicherweise mit den beobachteten Variablen interagieren - verborgen bleiben. In dieser Arbeit befassen wir uns mit dem Problem der Rekonstruktion und Vorhersage der zugrunde liegenden Dynamik komplexer Systeme mit Hilfe verschiedener datengestützter Ansätze. Im ersten Teil befassen wir uns mit dem umgekehrten Problem der Ableitung einer unbekannten Netzwerkstruktur komplexer Systeme, die Ausbreitungsphänomene widerspiegelt, aus beobachteten Ereignisreihen. Wir untersuchen die paarweise statistische Ähnlichkeit zwischen den Sequenzen von Ereigniszeitpunkten an allen Knotenpunkten durch Ereignissynchronisation (ES) und Ereignis-Koinzidenz-Analyse (ECA), wobei wir uns auf die Idee stützen, dass funktionale Konnektivität als Stellvertreter für strukturelle Konnektivität dienen kann. Im zweiten Teil konzentrieren wir uns auf die Rekonstruktion der zugrunde liegenden Dynamik komplexer Systeme anhand ihrer dominanten makroskopischen Variablen unter Verwendung verschiedener stochastischer Differentialgleichungen (SDEs). In dieser Arbeit untersuchen wir die Leistung von drei verschiedenen SDEs - der Langevin-Gleichung (LE), der verallgemeinerten Langevin-Gleichung (GLE) und dem Ansatz der empirischen Modellreduktion (EMR). Unsere Ergebnisse zeigen, dass die LE bessere Ergebnisse für Systeme mit schwachem Gedächtnis zeigt, während sie die zugrunde liegende Dynamik von Systemen mit Gedächtniseffekten und farbigem Rauschen nicht rekonstruieren kann. In diesen Situationen sind GLE und EMR besser geeignet, da die Wechselwirkungen zwischen beobachteten und unbeobachteten Variablen in Form von Speichereffekten berücksichtigt werden. Im letzten Teil dieser Arbeit entwickeln wir ein Modell, das auf dem Echo State Network (ESN) basiert und mit der PNF-Methode (Past Noise Forecasting) kombiniert wird, um komplexe Systeme in der realen Welt vorherzusagen. Unsere Ergebnisse zeigen, dass das vorgeschlagene Modell die entscheidenden Merkmale der zugrunde liegenden Dynamik der Klimavariabilität erfasst. / Modeling complex systems with large numbers of degrees of freedom have become a grand challenge over the past decades. Typically, only a few variables of complex systems are observed in terms of measured time series, while the majority of them – which potentially interact with the observed ones - remain hidden. Throughout this thesis, we tackle the problem of reconstructing and predicting the underlying dynamics of complex systems using different data-driven approaches. In the first part, we address the inverse problem of inferring an unknown network structure of complex systems, reflecting spreading phenomena, from observed event series. We study the pairwise statistical similarity between the sequences of event timings at all nodes through event synchronization (ES) and event coincidence analysis (ECA), relying on the idea that functional connectivity can serve as a proxy for structural connectivity. In the second part, we focus on reconstructing the underlying dynamics of complex systems from their dominant macroscopic variables using different Stochastic Differential Equations (SDEs). We investigate the performance of three different SDEs – the Langevin Equation (LE), Generalized Langevin Equation (GLE), and the Empirical Model Reduction (EMR) approach in this thesis. Our results reveal that LE demonstrates better results for systems with weak memory while it fails to reconstruct underlying dynamics of systems with memory effects and colored-noise forcing. In these situations, the GLE and EMR are more suitable candidates since the interactions between observed and unobserved variables are considered in terms of memory effects. In the last part of this thesis, we develop a model based on the Echo State Network (ESN), combined with the past noise forecasting (PNF) method, to predict real-world complex systems. Our results show that the proposed model captures the crucial features of the underlying dynamics of climate variability.

<p><br></p><p dir="ltr">The complexity of modern financial markets poses substantial challenges for analyzing time-series data, as traditional diffusion models often fail to capture the intricate dynamics of real-world market behavior. This dissertation develops data-driven, non-Markovian methodologies to overcome these limitations, enhancing the analysis of dependencies in financial and insurance data. The research employs advanced stochastic models and machine learning techniques to address critical phenomena in finance and insurance. Notable findings include the following: a Hawkes process framework is introduced to model cascading health transitions, capturing how past events amplify the likelihood of future occurrences (Chapter 3); a discrete-time Hawkes process is used to quantify time-varying lead-lag relationships between intraday and overnight returns, uncovering predictive dynamics in asset price movements (Chapter 4); and attention-based models are applied to high-dimensional, spatiotemporal limit order book (LOB) data, enabling robust analysis and forecasting of its complex structure and behavior (Chapter 5). These findings highlight the limitations of traditional Markovian models, particularly in representing memory-dependent systems, high-frequency data, and multi-state processes. By advancing non-Markovian methods, this dissertation provides practical tools for analyzing momentum effects, cascading health transitions, and intricate market microstructures. These contributions establish a robust analytical foundation for understanding memory-dependent dynamics in finance and insurance, addressing key limitations of Markovian assumptions and opening new avenues for research and application.</p>

The analysis of signals stemming from a physical system is crucial for the experimental investigation of the underlying dynamics that drives the system itself. The field of time series analysis comprises a wide variety of techniques developed with the purpose of characterizing signals and, ultimately, of providing insights on the phenomena that govern the temporal evolution of the generating system. A renowned example in this field is given by spectral analysis: the use of Fourier or Laplace transforms to bring time-domain signals into the more convenient frequency space allows to disclose the key features of linear systems. A more complex scenario turns up when nonlinearity intervenes within a system's dynamics. Nonlinear coupling between a system's degrees of freedom brings about interesting dynamical regimes, such as self-sustained periodic (though anharmonic) oscillations ("limit cycles"), or quasi-periodic evolutions that exhibit sharp spectral lines while lacking strict periodicity ("limit tori"). Among the consequences of nonlinearity, the onset of chaos is definitely the most fascinating one. Chaos is a dynamical regime characterized by unpredictability and lack of periodicity, despite being generated by deterministic laws. Signals generated by chaotic dynamical systems appear as irregular: the corresponding spectra are broad and flat, prediction of future values is challenging, and evolutions within the systems' state spaces converge to strange attractor sets with noninteger dimensionality. Because of these properties, chaotic signals can be mistakenly classified as noise if linear techniques such as spectral analysis are used. The identification of chaos and its characterization require the assessment of dynamical invariants that quantify the complex features of a chaotic system's evolution. For example, Lyapunov exponents provide a marker of unpredictability; the estimation of attractor dimensions, on the other hand, highlights the unconventional geometry of a chaotic system's state space. Nonlinear time series analysis techniques act directly within the state space of the system under investigation. However, experimentally, full access to a system's state space is not always available. Often, only a scalar signal stemming from the dynamical system can be recorded, thus providing, upon sampling, a scalar sequence. Nevertheless, by virtue of a fundamental theorem by Takens, it is possible to reconstruct a proxy of the original state space evolution out of a single, scalar sequence. This reconstruction is carried out by means of the so-called embedding procedure: m-dimensional vectors are built by picking successive elements of the scalar sequence delayed by a lag L. On the other hand, besides posing some necessary conditions on the integer embedding parameters m and L, Takens' theorem does not provide any clue on how to choose them correctly. Although many optimal embedding criteria were proposed, a general answer to the problem is still lacking. As a matter of fact, conventional methods for optimal embedding are flawed by several drawbacks, the most relevant being the need for a subjective evaluation of the outcomes of applied algorithms. Tackling the issue of optimally selecting embedding parameters makes up the core topic of this thesis work. In particular, I will discuss a novel approach that was pursued by our research group and that led to the development of a new method for the identification of suitable embedding parameters. Rather than most conventional approaches, which seek a single optimal value for m and L to embed an input sequence, our approach provides a set of embedding choices that are equivalently suitable to reconstruct the dynamics. The suitability of each embedding choice m, L is assessed by relying on statistical testing, thus providing a criterion that does not require a subjective evaluation of outcomes. The starting point of our method are embedding-dependent correlation integrals, i.e. cumulative distributions of embedding vector distances, built out of an input scalar sequence. In the case of Gaussian white noise, an analytical expression for correlation integrals is available, and, by exploiting this expression, a gauge transformation of distances is introduced to provide a more convenient representation of correlation integrals. Under this new gauge, it is possible to test—in a computationally undemanding way—whether an input sequence is compatible with Gaussian white noise and, subsequently, whether the sequence is compatible with the hypothesis of an underlying chaotic system. These two statistical tests allow ruling out embedding choices that are unsuitable to reconstruct the dynamics. The estimation of correlation dimension, carried out by means of a newly devised estimator, makes up the third stage of the method: sets of embedding choices that provide uniform estimates of this dynamical invariant are deemed to be suitable to embed the sequence.The method was successfully applied to synthetic and experimental sequences, providing new insight into the longstanding issue of optimal embedding. For example, the relevance of the embedding window (m-1)L, i.e. the time span covered by each embedding vector, is naturally highlighted by our approach. In addition, our method provides some information on the adequacy of the sampling period used to record the input sequence.The method correctly distinguishes a chaotic sequence from surrogate ones generated out of it and having the same power spectrum. The technique of surrogate generation, which I also addressed during my Ph. D. work to develop new dedicated algorithms and to analyze brain signals, allows to estimate significance levels in situations where standard analytical algorithms are unapplicable. The novel embedding approach being able to tell apart an original sequence from surrogate ones shows its capability to distinguish signals beyond their spectral—or autocorrelation—similarities.One of the possible applications of the new approach concerns another longstanding issue, namely that of distinguishing noise from chaos. To this purpose, complementary information is provided by analyzing the asymptotic (long-time) behaviour of the so-called time-dependent divergence exponent. This embedding-dependent metric is commonly used to estimate—by processing its short-time linearly growing region—the maximum Lyapunov exponent out of a scalar sequence. However, insights on the kind of source generating the sequence can be extracted from the—usually overlooked—asymptotic behaviour of the divergence exponent. Moreover, in the case of chaotic sources, this analysis also provides a precise estimate of the system's correlation dimension. Besides describing the results concerning the discrimination of chaotic systems from noise sources, I will also discuss the possibility of using the related correlation dimension estimates to improve the third stage of the method introduced above for the identification of suitable embedding parameters. The discovery of chaos as a possible dynamical regime for nonlinear systems led to the search of chaotic behaviour in experimental recordings. In some fields, this search gave plenty of positive results: for example, chaotic dynamics was successfully identified and tamed in electronic circuits and laser-based optical setups. These two families of experimental chaotic systems eventually became versatile tools to study chaos and its possible applications. On the other hand, chaotic behaviour is also looked for in climate science, biology, neuroscience, and even economics. In these fields, nonlinearity is widespread: many smaller units interact nonlinearly, yielding a collective motion that can be described by means of few, nonlinearly coupled effective degrees of freedom. The corresponding recorded signals exhibit, in many cases, an irregular and complex evolution. A possible underlying chaotic evolution—as opposed to a stochastic one—would be of interest both to reveal the presence of determinism and to predict the system's future states. While some claims concerning the existence of chaos in these fields have been made, most results are debated or inconclusive. Nonstationarity, low signal-to-noise ratio, external perturbations and poor reproducibility are just few among the issues that hinder the search of chaos in natural systems. In the final part of this work, I will briefly discuss the problem of chasing chaos in experimental recordings by considering two example sequences, the first one generated by an electronic circuit and the second one corresponding to recordings of brain activity. The present thesis is organized as follows. The core concepts of time series analysis, including the key features of chaotic dynamics, are presented in Chapter 1. A brief review of the search for chaos in experimental systems is also provided; the difficulties concerning this quest in some research fields are also highlighted. Chapter 2 describes the embedding procedure and the issue of optimally choosing the related parameters. Thereupon, existing methods to carry out the embedding choice are reviewed and their limitations are pointed out. In addition, two embedding-dependent nonlinear techniques that are ordinarily used to characterize chaos, namely the estimation of correlation dimension by means of correlation integrals and the assessment of maximum Lyapunov exponent, are presented. The new approach for the identification of suitable embedding parameters, which makes up the core topic of the present thesis work, is the subject of Chapter 3 and 4. While Chapter 3 contains the theoretical outline of the approach, as well as its implementation details, Chapter 4 discusses the application of the approach to benchmark synthetic and experimental sequences, thus illustrating its perks and its limitations. The study of the asymptotic behaviour of the time-dependent divergent exponent is presented in Chapter 5. The alternative estimator of correlation dimension, which relies on this asymptotic metric, is discussed as a possible improvement to the approach described in Chapters 3, 4. The search for chaos out of experimental data is discussed in Chapter 6 by means of two examples of real-world recordings. Concluding remarks are finally drawn in Chapter 7.

Объект исследования – фреймворки анализа временных рядов. Цель работы – сравнительная оценка преимуществ и недостатков фреймворков анализа временных рядов по определенному набору критериев. Методы исследования: 1) анализ документации и исходного кода фреймворков; 2) проведение бэктестинг замеров. Результаты работы: 1) получены и проанализированы результаты замеров точности и скорости работы методов: ARIMA, Prophet, TBATS, ETS; 2) по результатам анализа выявлено реализации каких методов в каких фреймворках показывают лучшую точность и скорость работы. / The object of study is time series analysis frameworks. The purpose of the work is a comparative assessment of the advantages and disadvantages of time series analysis frameworks based on a specific set of criteria. Research methods: 1) analysis of documentation and source code of frameworks; 2) performing of backtesting measurements. Work results: 1) the results of measuring the accuracy and execution time of the methods: ARIMA, Prophet, TBATS, ETS were obtained and analysed; 2) based on the results of the analysis, implementations of which methods in which frameworks show the best accuracy and speed were identified.

Information extraction from large corpora can be a useful tool for many applications in industry and academia. For instance, political communication science has just recently begun to use the opportunities that come with the availability of massive amounts of information available through the Internet and the computational tools that natural language processing can provide. We give a linguistically motivated interpretation of topic modeling, a state-of-the-art algorithm for extracting latent semantic sets of words from large text corpora, and extend this interpretation to cover issues and issue-cycles as theoretical constructs coming from political communication science. We build on a dynamic topic model, a model whose semantic sets of words are allowed to evolve over time governed by a Brownian motion stochastic process and apply a new form of analysis to its result. Generally this analysis is based on the notion of volatility as in the rate of change of stocks or derivatives known from econometrics. We claim that the rate of change of sets of semantically related words can be interpreted as issue-cycles, the word sets as describing the underlying issue. Generalizing over the existing work, we introduce dynamic topic models that are driven by general (Brownian motion is a special case of our model) Gaussian processes, a family of stochastic processes defined by the function that determines their covariance structure. We use the above assumption and apply a certain class of covariance functions to allow for an appropriate rate of change in word sets while preserving the semantic relatedness among words. Applying our findings to a large newspaper data set, the New York Times Annotated corpus (all articles between 1987 and 2007), we are able to identify sub-topics in time, \\\\textit{time-localized topics} and find patterns in their behavior over time. However, we have to drop the assumption of semantic relatedness over all available time for any one topic. Time-localized topics are consistent in themselves but do not necessarily share semantic meaning between each other. They can, however, be interpreted to capture the notion of issues and their behavior that of issue-cycles.

Thesis (MScEng)--University of Stellenbosch, 2000. / ENGLISH ABSTRACT: Air pollution is a major concern III the Cape Metropole. A major contributor to the air pollution problem is road transport. For this reason, a national vehicle emissions study is in progress with the aim of developing a national policy regarding motor vehicle emissions and control. Such a policy could bring about vehicle emission control and regulatory measures, which may have far-reaching social and economic effects. Air pollution models are important tools 10 predicting the effectiveness and the possible secondary effects of such policies. It is therefore essential that these models are fundamentally sound to maintain a high level of prediction accuracy. Complex air pollution models are available, but they require spatial, time-resolved information of emission sources and a vast amount of processing power. It is unlikely that South African cities will have the necessary spatial, time-resolved emission information in the near future. An alternative air pollution model is one that is based on the Gaussian Plume Model. This model, however, relies on gross simplifying assumptions that affect model accuracy. It is proposed that statistical and mathematical analysis techniques will be the most viable approach to modelling air pollution in the Cape Metropole. These techniques make it possible to establish statistical relationships between pollutant emissions, meteorological conditions and pollutant concentrations without gross simplifying assumptions or excessive information requirements. This study investigates two analysis techniques that fall into the aforementioned category, namely, Non-linear Time Series Analysis (specifically, the method of delay co-ordinates) and Singular Spectrum Analysis (SSA). During the past two decades, important progress has been made in the field of Non-linear Time Series Analysis. An entire "toolbox" of methods is available to assist in identifying non-linear determinism and to enable the construction of predictive models. It is argued that the dynamics that govern a pollution system are inherently non-linear due to the strong correlation with weather patterns and the complexity of the chemical reactions and physical transport of the pollutants. In addition to this, a statistical technique (the method of surrogate data) showed that a pollution data set, the oxides of Nitrogen (NOx), displayed a degree of non-linearity, albeit that there was a high degree of noise contamination. This suggested that a pollution data set will be amenable to non-linear analysis and, hence, Non-linear Time Series Analysis was applied to the data set. SSA, on the other hand, is a linear data analysis technique that decomposes the time series into statistically independent components. The basis functions, in terms of which the data is decomposed, are data-adaptive which makes it well suited to the analysis of non-linear systems exhibiting anharmonic oscillations. The statistically independent components, into which the data has been decomposed, have limited harmonic content. Consequently, these components are more amenable to prediction than the time series itself. The fact that SSA's ability has been proven in the analysis of short, noisy non-linear signals prompted the use of this technique. The aim of the study was to establish which of these two techniques is best suited to the modelling of air pollution data. To this end, a univariate model to predict NOx concentrations was constructed using each of the techniques. The prediction ability of the respective model was assumed indicative of the accuracy of the model. It was therefore used as the basis against which the two techniques were evaluated. The procedure used to construct the model and to quantify the model accuracy, for both the Non-linear Time Series Analysis model and the SSA model, was consistent so as to allow for unbiased comparison. In both cases, no noise reduction schemes were applied to the data prior to the construction of the model. The accuracy of a 48-hour step-ahead prediction scheme and a lOO-hour step-ahead prediction scheme was used to compare the two techniques. The accuracy of the SSA model was markedly superior to the Non-linear Time Series model. The paramount reason for the superior accuracy of the SSA model is its adept ability to analyse and cope with noisy data sets such as the NOx data set. This observation provides evidence to suggest that Singular Spectrum Analysis is better suited to the modelling of air pollution data. It should therefore be the analysis technique of choice when more advanced, multivariate modelling of air pollution data is carried out. It is recommended that noise reduction schemes, which decontaminate the data without destroying important higher order dynamics, should be researched. The application of an effective noise reduction scheme could lead to an improvement in model accuracy. In addition to this, the univariate SSA model should be extended to a more complex multivariate model that explicitly encompasses variables such as traffic flow and weather patterns. This will explicitly expose the inter-relationships between the variables and will enable sensitivity studies and the evaluation of a multitude of scenarios. / AFRIKAANSE OPSOMMING: Die hoë vlak van lugbesoedeling in die Kaapse Metropool is kommerwekkend. Voertuie is een van die hoofoorsake, en as gevolg hiervan word 'n landswye ondersoek na voertuigemissie tans onderneem sodat 'n nasionale beleid opgestel kan word ten opsigte van voertuigemissie beheer. Beheermaatreëls van so 'n aard kan verreikende sosiale en ekonomiese uitwerkings tot gevolg hê. Lugbesoedelingsmodelle is van uiterste belang in die voorspelling van die effektiwiteit van moontlike wetgewing. Daarom is dit noodsaaklik dat hierdie modelle akkuraat is om 'n hoë vlak van voorspellingsakkuraatheid te handhaaf. Komplekse modelle is beskikbaar, maar hulle verg tyd-ruimtelike opgeloste inligting van emmissiebronne en baie berekeningsvermoë. Dit is onwaarskynlik dat Suid-Afrika in die nabye toekoms hierdie tydruimtelike inligting van emissiebronne gaan hê. 'n Alternatiewe lugbesoedelingsmodel is dié wat gebaseer is op die "Guassian Plume". Hierdie model berus egter op oorvereenvoudigde veronderstellings wat die akkuraatheid van die model beïnvloed. Daar word voorgestel dat statistiese en wiskundige analises die mees lewensvatbare benadering tot die modellering van lugbesoedeling in die Kaapse Metropool sal wees. Hierdie tegnieke maak dit moontlik om 'n statistiese verwantskap tussen besoedelingsbronne, meteorologiese toestande en besoedeling konsentrasies te bepaal sonder oorvereenvoudigde veronderstellings of oormatige informasie vereistes. Hierdie studie ondersoek twee analise tegnieke wat in die bogenoemde kategorie val, naamlik, Nie-lineêre Tydreeks Analise en Enkelvoudige Spektrale Analise (ESA). Daar is in die afgelope twee dekades belangrike vooruitgang gemaak in die studieveld van Nie-lineêre Tydreeks Analise. 'n Volledige stel metodes is beskikbaar om nie-lineêriteit te identifiseer en voorspellingsmodelle op te stel. Dit word geredeneer dat die dinamika wat 'n besoedelingsisteem beheer nie-lineêr is as gevolg van die sterk verwantskap wat dit toon met weerpatrone asook die kompleksiteit van die chemiese reaksies en die fisiese verplasing van die besoedelingstowwe. Bykomend verskaf 'n statistiese tegniek (die metode van surrogaatdata) bewyse dat 'n lugbesoedelingsdatastel, die okside van Stikstof (NOx), melineêre gedrag toon, alhoewel daar 'n hoë geraasvlak is. Om hierdie rede is die besluit geneem om Nie-lineêre Tydreeks Analise aan te wend tot die datastel. ESA daarenteen, is 'n lineêre data analise tegniek. Dit vereenvoudig die tydreeks tot statistiese onafhanklike komponente. Die basisfunksies, in terme waarvan die data vereenvoudig is, is data-aanpasbaar en dit maak hierdie tegniek gepas vir die analise van nielineêre sisteme. Die statisties onafhanklike komponente het beperkte harmoniese inhoud, met die gevolg dat die komponente aansienlik makliker is om te voorspel as die tydreeks self. ESA se effektiwitiet is ook al bewys in die analise van kort, hoë-graas nie-lineêre seine. Om hierdie redes, is ESA toegepas op die lugbesoedelings data. Die doel van die ondersoek was om vas te stel watter een van die twee tegnieke meer gepas is om lugbesoedelings data te analiseer. Met hierdie doelwit in sig, is 'n enkelvariaat model opgestel om NOx konsentrasies te voorspel met die gebruik van elk van die tegnieke. Die voorspellingsvermoë van die betreklike model is veronderstelom as 'n maatstaf van die model se akkuraatheid te kan dien en dus is dit gebruik om die twee modelle te vergelyk. 'n Konsekwente prosedure is gevolg om beide die modelle te skep om sodoende invloedlose vergelyking te verseker. In albei gevalle was daar geen geraasverminderings-tegnieke toegepas op die data nie. Die akuraatheid van 'n 48-uur voorspellingsmodel en 'n 100-uur voorspellingsmodel was gebruik vir die vergelyking van die twee tegnieke. Daar is bepaal dat die akkuraatheid van die ESA model veel beter as die Nie-lineêre Tydsreeks Analise is. Die hoofrede vir die ESA se hoër akkuraatheid is die model se vermoë om data met hoë geraasvlakke te analiseer. Hierdie ondersoek verskaf oortuigende bewyse dat Enkelvoudige Spektrale Analiese beter gepas is om lugbesoedelingsdata te analiseer en gevolglik moet hierdie tegniek gebruik word as meer gevorderde, multivariaat analises uitgevoer word. Daar word aanbeveel dat geraasverminderings-tegnieke, wat die data kan suiwer sonder om belangrike hoë-orde dinamika uit te wis, ondersoek moet word. Hierdie toepassing van effektiewe geraasverminderings-tegniek sal tot 'n verbetering in model-akkuraatheid lei. Aanvullend hiertoe, moet die enkele ESA model uitgebrei word tot 'n meer komplekse multivariaat model wat veranderlikes soos verkeersvloei en weerpatrone insluit. Dit sal die verhoudings tussen veranderlikes ten toon stel en sal sensitiwiteit-analises en die evaluering van menigte scenarios moontlik maak.

Thesis (MComm (Business Management))--University of Stellenbosch, 2007. / ENGLISH ABSTRACT: his study aims to investigate whether the phenomena found by Shnoll et al. when applying histogram pattern analysis techniques to stochastic processes from chemistry and physics are also present in financial time series, particularly exchange rate and index data. The phenomena are related to fine structure of non-smoothed frequency distributions drawn from statistically insufficient samples of changes and their patterns in time. Shnoll et al. use the notion of macroscopic fluctuations to explain the behaviour of sequences of histograms. Histogram patterns in time adhere to several laws that could not be detected when using time series analysis methods. In this study general approaches are reviewed that may be used to model financial markets and the volatility of price processes in particular. Special emphasis is placed on the modelling of highfrequency data sets and exchange rate data. Following previous studies of the Shnoll phenomena from other fields, different steps of the histogram sequence analysis are carried out to determine whether the findings of Shnoll et al. could also be applied to financial market data. The findings of this thesis widen the understanding of time varying volatility and can aid in financial risk measurement and management. Outcomes of the study include an investigation of time series characteristics in terms of the formation of discrete states, the detection of the near zone effect as proclaimed by Shnoll et al., the periodic recurrence of histogram shapes as well as the synchronous variation in data sets measured in the same time intervals.