Thesis (M. Sc. (Statistics)) -- University of Limpopo, 2021 / The effects of ozone depletion on climate change has, in recent years, become a reality, impacting on changes in rainfall patterns and severity of extreme floods or extreme droughts. The majority of people across the entire African continent live in semi-arid and drought-prone areas. Extreme droughts are prevalent in Somalia and eastern Africa, while life-threatening floods are common in Mozambique and some parts of other SADC (Southern African Development Community) countries. Research has cautioned that climate change in South Africa might lead to increased temperatures and reduced amounts of rainfall, thereby altering their timing and putting more pressure on the country’s scarce water resources, with implications for agriculture, employment and food security. The average annual rainfall for South Africa is about 464mm, falling far below the average annual global rainfall of 860mm. The Limpopo Province, which is one of the nine provinces in South Africa, and of interest to this study, is predominantly agrarian, basically relying on availability of water, with rainfall being the major source for water supply. It is, therefore, pertinent that the rainfall pattern in the province be monitored effectively to ascertain the rainy period for farming activities and other uses. Modelling and forecasting rainfall have been studied for a long time worldwide. However, from time to time, researchers are always looking for new models that can predict rainfall more accurately in the midst of climate change and capture the underlying dynamics such as seasonality and the trend, attributed to rainfall. This study employed Exponetial Smoothing (ETS) State Space and Seasonal Autoregressive Integrated Moving Average (SARIMA) models and compared their forecasting ability using root mean square error (RMSE). Both models were used to capture the sporadic behaviour of rainfall. These two models have been widely applied to climatic data by many scholars and adjudged to perform creditably well. In an attempt to find a suitable prediction model for monthly rainfall patterns in Limpopo Province, data ranging from January 1900 to December 2015, for seven weather stations: Macuville Agriculture, Mara Agriculture, Marnits, Groendraal, Letaba, Pietersburg Hospital and Nebo, were analysed. The results showed that the two models were adequate in predicting rainfall patterns for the different stations in the Limpopo Province. / National Research Foundation (NRF)

This thesis is dedicated to the application of machine learning methods to algorithmic trading. We take inspiration from intraday traders and implement a system that predicts future price based on candlestick patterns and technical indicators. Using forex and US stocks tick data we create multiple aggregated bar representations. From these bars we construct original features based on candlestick pattern clustering by K-Means and long-term features derived from standard technical indicators. We then setup regression and classification tasks for Extreme Gradient Boosting models. From their predictions we extract buy and sell trading signals. We perform experiments with eight different configurations over multiple assets and trading strategies using walk-forward validation. The results report Sharpe ratios and mean profits of all the combinations. We discuss the results and recommend suitable configurations. In overall our strategies outperform randomly selected strategies. Furthermore, we provide and discuss multiple opportunities for further research.

Förevarande studie undersöker möjligheten att förutsäga aktierörelse på en dagligbasis med sentimentanalys av inlägg från ett svenskt aktieforum. Sentimentanalys används för att finna subjektivitet i form av känslor (sentiment) ur text. Textdata extraherades från ett svenskt aktieforum för att förutsäga aktierörelsen för den relaterade aktien. All data aggregerades inom en bestämd tidsperiod på två år. Undersökningen utnyttjade maskininlärning för att träna tre maskininlärningsmodeller med textdata och aktiedata. Resultatet påvisade ingen tydlig korrelation mellan sentiment och aktierörelse. Vidare uppnåddes inte samma resultat som tidigare arbeten inom området. Den högst uppnådda noggrannheten med modellerna beräknades till 64%. / The present study examines the possibility of predicting stock movement on a daily basis with sentiment analysis of posts in a swedish stock trading forum. Sentiment analysis is used to find subjectivity in the form of emotions (sentiment) from text. Textdata was extracted from a stock forum to predict the share movement of the related share. All data was aggregated within a fixed period of two years. The analysis utilizes machine learning to train three machine learning models with textdata and stockdata. The result showed no clear correlation between sentiment and stock movement. Furthermore, the result was not able to replicate accuracy as previous work in the field. The highest accuracy achieved with the models was calculated at 64%.

Grundvatten och dess varierande nivåer kan potentiellt få en stor inverkan både på byggnaderoch dess omgivning och kan innebära risker som upplyftande krafter, skred och ras. Baseratpå detta är det av vikt att kunna förutsäga extrema grundvattennivåer, kallat dimensionerandegrundvattennivåer. Däremot görs sällan mätningar under en längre tid, vilket krävs för att fastställasannolikheten av en viss grundvattennivå. För att kunna prognostisera den dimensionerandegrundvattennivån har den så kallade Chalmersmodellen utvecklats. Modellen utgår från attsätta korta mätningar från ett grundvattenrör vid en observationsplats (observationsrör) i relation till en lång mätserie från ett grundvattenrör vid en referensplats (referensrör). Enligtmetoden ska val av referensrör baseras på att det är likartade förhållanden mellan de två platserna, att de ligger inom 50 km från varandra och att mätningar i referensröret utförts i mer än 20 år. Denna studie syftar att utreda med vilken tillförlitlighet som Chalmersmodellen kan prognostisera grundvattennivåer som kan förekomma inom en viss återkomsttid. Fokus är på hur valet av referensrör som är placerade vid olikartade hydrogeologiska förhållanden påverkar Chalmersmodellens resultat. Studien utförs som en fallstudie, med utgångspunkt i utbyggnaden av tunnelbanan i Stockholm vid Sockenplan och Station Sofia. Utgångspunkten i Chalmersmodellen är att använda grundvattennivåmätningar från observationsplatsen tillsammans med mätningar från en ostörd miljö vid en referensplats. Beräkningar görs genom att utföra databehandling och beräkningar i Python i enlighet med beskrivningar från Chalmersmodellen och utvärderas genom att jämföras mot en liknande metod kallad extremvärdesanalys. Karakterisering av platserna vid observationsrören och referensrören används för att utvärdera hur stor inverkan olika hydrogeologiska egenskaper (akvifertyp och topografiskt läge) har på beräkningarna av den dimensionerande grundvattennivån. Resultaten visar att Chalmersmodellen generellt underskattar dimensionerande grundvattennivåer. Modellen har även varierande storleksordning av noggrannheten och därmed är det svårt att fastställa förväntad noggrannhet med Chalmersmodellen. Studien visar även att om observationsrör och referensrör är placerade vid en sluten akvifer kan en högre tillförlitlighet förväntas och osäkerheten i tillförlitligheten tycks öka för öppna akviferer. Slutligen om referensrör och observationsrör väljs utifrån att likartade hydrogeologiska egenskaper och samvariation mellan respektive grundvattennivåer, kan högre precision förväntas enligt denna studie. / Groundwater can potentially have a great impact on both constructions and the surrounding areas, and high groundwater levels can involve risks such as uplifting forces and landslide. Due to these risks it is important to predict and estimate the probability of extreme groundwater levels. However, when the necessary long term measurements are not available alternative methods are needed, like the Chalmers model. The Chalmers model is used for calculating extreme ground water levels, by combining a short measurement series from an observation well with the data from a reference well. For the results to be as accurate as possible, the two wells must share similar characteristics. The aim of this study is to investigate the Chalmers model when predicting the groundwater level for a specific return period. Focus will be on how the choice of different reference wells, with different characteristics, will influence the accuracy of the model.  A case study will be conducted on two station sites (Sockenplan and Station Sofia) for the extension of the metro in the southern part of Stockholm, Sweden, upon which the Chalmer model will be implemented. The different characteristics of the obeservation and reference wells are tested to evaluate the accuracy of the model. The accuracy will be evaluated by using extreme value analysis as an alternative calculation model, assumed to be more precise, and compare the difference in extreme groundwater levels. The measurements used as reference in the Chalmers model are public data from The Geological Survey of Sweden, SGU, for groundwater levels. Data processing and calculations are performed in python. This study highlights the difficulties in determining the accuracy of the Chalmers model when predicting extreme groundwater levels, and no specific expected accuracy has been determined. Generally, the model appears to underestimate extreme grounwater levels. Furthermore, if the observation well and reference well are located by a confined aquifer and between inflow- and outflow areas, a higher precision can be expected. The uncertainty of the model increases with an unconfined aquifer. The results also imply that if the reference well and the observation well are selected based on similar hydrogeological characteristics, a covariation of groundwater levels over time and between highest and lowest level, a higher accuracy can be expected.

Die Erforschung von Gravitationswellen hat unsere Sicht auf das Universum revolutioniert. Mit dem bevorstehenden Start von LISA, einem Weltraum-Gravitationswellendetektor, und neuen Berichten über Hinweise auf einen Gravitationswellenhintergrund im Nanohertz-Bereich aus Pulsar Timing Array (PTA)-Experimenten, eröffnen sich neue Möglichkeiten und Herausforderungen. Diese Dissertation entwickelt innovative Datenanalysetechniken und Wellenformmodelle, um Erkenntnisse aus diesen Beobachtungen zu gewinnen. Ein Schwerpunkt liegt auf der Untersuchung von Extreme Mass Ratio Inspirals (EMRIs) durch LISA. Diese Quellen bestehen aus kleinen, kompakten Objekten, die sich um ein zentrales Schwarzes Loch bewegen. Die Wellenformen von EMRIs bieten die Möglichkeit präziser Parametermessungen, sind jedoch aufgrund ihrer langen Signaldauer und harmonischen Komplexität schwer zu berechnen. Wir präsentieren die Implementierung einsatzbereiter EMRI-Wellenformen im Frequenzbereich für Grafikprozessoren (GPUs) und zentrale Recheneinheiten (CPUs). Zudem untersuchen wir das wissenschaftliche Potenzial von EMRIs innerhalb von Akkretionsscheiben, erforschen den Einfluss von Umwelteffekten mittels bayesianischer Methoden und bewerten die Multimessenger-Aussichten dieser Systeme. Im PTA-Bereich entwickeln wir Methoden zur Optimierung der Datenkombinationen für PTA-Analysen und tragen zum European Pulsar Timing Array bei, indem wir alternative Sampling-Pipelines für die Analyse von Gravitationswellenhintergründen und individuellen Quellen implementieren. Mit transdimensionalen Sampling-Methoden suchen wir nach einzelnen supermassiven Schwarzen Löchern und bewerten deren Signifikanz. Diese Dissertation trägt zur Weiterentwicklung der Gravitationswellenastronomie bei, indem sie neue Methoden und Modelle entwickelt, die tiefere Einblicke in die kosmischen Phänomene ermöglichen, die von LISA- und PTA-Beobachtungen erfasst werden. / Gravitational wave astronomy has reshaped our understanding of the cosmos. As we look towards the future launch of LISA, a space-based gravitational wave detector, and analyze recent evidence of a nanohertz gravitational wave background from Pulsar Timing Array (PTA) experiments, new opportunities and challenges emerge. This thesis delves into developing novel data analysis techniques and waveform models to extract information from these observations. Focusing on LISA, we delve into Extreme Mass Ratio Inspirals (EMRIs). These sources consist of small compact objects spiralling into massive black holes at the centres of galaxies. Their observations are expected to provide precise parameter measurements for these systems. However, EMRI waveform generation poses challenges due to the long signal duration and large harmonic content. For the first time, we provide a fast implementation of EMRI waveforms in the frequency domain, suitable for both graphics processing units (GPUs) and central processing units (CPUs). In addition, we explore the scientific potential of EMRIs embedded in accretion disks. Employing Bayesian inference, we investigate the measurability of environmental effects and explore these systems' multimessenger prospects. Transitioning to PTA, we develop methods to optimize data combinations for PTA analyses. We present our contributions to the second data release of the European Pulsar Timing Array collaboration, which consists of implementing alternative sampling pipelines for gravitational wave background and individual source analyses. Using trans-dimensional sampling methods, we search for individual supermassive black hole binaries and assess their significance. The burgeoning field of gravitational wave astronomy has the potential to transform our understanding of the Universe. The work in this thesis develops new approaches that will facilitate the delivery of the best possible scientific results from current and future gravitational wave observations.

Convective snow bands develop commonly over the open water surface of lakes or seas when cold airgets advected from a continent. Enhanced heat and moisture fluxes from the comparatively warm waterbody trigger shallow convection and an unstable boundary layer builds up. Relatively strong wind canorganize this convection into wind-parallel quasi-stationary cloud bands with moving individual cells.Depending on various factors like the horizontal wind, the vertical shear or the shape of the coast, thosecloud bands can form of different strength and structure. When the air mass meets the coast orographicforcing causes horizontal convergence and vertical lifting intensifies the precipitation at the coast. If thewind direction stays constant for several days a single snow band would accumulate its precipitation ina very restricted region and cause locally a significant increase in snow depth. This process leads in thecold season repeatedly to severe precipitation events at the Swedish east coast. Large amounts of snowalong with strong wind speeds can cause serious problems for traffic and infrastructure.Two different cases of convective snow bands in the Baltic Sea area were selected to simulate theassociated atmospheric conditions with a total of five different model systems. The atmosphere climatemodel RCA has been used independently at default settings as well as with increased resolution on avertical and a horizontal scale and furthermore coupled either to the ice-ocean model NEMO or the wavemodel component WAM.Comparing all models the crucial parameters like wind, temperature, heat fluxes, and precipitationvary generally in a reasonable range. However, the model systems show systematical differences amongthemselves. The strongest 10 meter wind speeds can be observed for both RCA models with increasedresolution. The RCA-WAM simulation shows its wind enhancement during the snow band event witha time shift to the other models by several hours. The mean directional wind shear above the Gulf ofBothnia, the snow band’s region of origin, is for all models small. The warmest sea surface temperaturesare reached by the RCA-NEMO simulation, which as a result also stands out for its most intense heatfluxes in both sensible and latent heat. Both high resolution RCA models as well as RCA-NEMO givethe most remarkable local precipitation rates. The original RCA and RCA-WAM simulate significantlyless snowfall. Local comparison with SMHI station measurements show that the models represent thetrend of wind, temperature and precipitation evolution well. However, all models decelerate the air masstoo rapidly when meeting the coast. Moreover, it remains a challenge to simulate the exact time andlocation of the extreme precipitation.The coupling of the atmosphere model with the ice-ocean model as well as the increased resolution ofthe atmospheric component have been observed to show great improvements in the model performanceand are suggested for future research work to be used in combination with each other for the regionalmodelling of convective snow bands in the Baltic Sea area.

Gender is a constantly debated subject, especially within the world of sports. The representation of athletes in the media is dominated by the males. It is often that the athletes are portrayed on the basis of their sex and gender. With the extreme skiing being a new and modern sport, should it not be autonomous from gender? This study aims to examine whether and if so how the cover design differ between female and male extreme skiing athletes and how it affects the professional skiers. A semiotic analysis was used on the covers of the Swedish skier’s magazine Åka Skidor and interviews were held with some of Sweden’s professional extreme skiers using a hermeneutic approach. The theoretical framework used for this study was poststructuralism, poststructuralist feminism and gender theory. The semiotic analysis showed that there is in fact a difference in both representation and how the skiers are portrayed on the covers of Åka Skidor. The interviews that were held resulted in three themes to answer the aim of this study. They were; the climate of extreme skiing, extreme skiing in media and the future of extreme skiing. The skiers had acknowledged that there is a difference between females and males when it comes to media representation and how they are portrayed. Although the explanation for this differs between the skiers they all mentioned the power of sponsors and sponsorship. However; the issue with athletes being portrayed and represented different based on their gender is not important enough to debate within the world of extreme skiing today. Therefore, it can be concluded that extreme skiing will probably not be autonomous from gender in the near future.

The alkali elements at ambient conditions are well described by the nearly-free electron (NFE) model, yet show a remarkable departure from this “simple” behaviour with increasing pressure. Low-symmetry complex structures are observed in all, and anomalous melting has been observed in lithium (Li), sodium (Na), rubidium (Rb), and caesium (Cs). In this Thesis, static and dynamic compression techniques have been used to investigate the high-pressure high-temperature behaviour of the alkali elements potassium (K) and Na. Utilising diamond anvil pressure cells and external resistive heating, both in-air and in-vacuum, the melting curve of K has been determined to 24 GPa and 750 K, and is found to be remarkably similar to that of Na, but strikingly different to that reported previously. Furthermore, there is some evidence to suggest that a change in the compressibility of liquid-K occurs at lower pressures than the solid-solid phase transitions, perhaps indicating structural transitions occurring in the liquid phase, similar to those in the underlying solid. This could suggest a mechanism to explain the anomalous melting behaviour observed. Previous ab initio computational studies indicate that the unusual melting curve of Na arises due to structural and electronic transitions occurring in the liquid, mirroring those found in the underlying solid at higher pressures. The discovery that the melting curve of K is very similar to that of Na suggests that the same physical phenomena predicted for Na could be responsible for the high-pressure melting behaviour observed in K. The tI19 phase of K, observed above 20 GPa at 300 K, is a composite incommensurate host-guest structure consisting of 1D chains of guest atoms surrounded by a tetragonal host framework. Along the unique c-axis, the host and guest are incommensurate with each other. During the melting studies described above, it was observed that with increasing temperature, the weaker-bonded guest chains become more disordered while the host structure remains unchanged. To investigate and characterise this order-disorder transition, in situ synchrotron X-ray diffraction studies were conducted on single-crystal and quasi-single crystal samples of tI19-K. An order-disorder phase line has been mapped out to 50 GPa and 650 K. Perhaps the most striking departure from NFE behaviour in the alkali elements is observed in Na at pressures above 200 GPa where it transforms to a transparent electrical insulator. This phase is a so-called elemental “electride”, which may be thought of as being pseudo-ionically bonded. Electrides are predicted to exist in many elements, but at pressures far beyond the current capabilities of static pressure techniques. Utilising laser-driven quasi-isentropic compression techniques, dynamic compression experiments were performed on Na to see if it is possible to observe this electride phase under the timescales of dynamic compression experiment (ns). Optical velocimetry and reflectivity of the sample were measured directly to determine pressure and monitor the on-set of the transparent phase, respectively.

We compare the traditional GARCH models with a semiparametric approach based on extreme value theory and find that the semiparametric approach yields more accurate predictions of Value-at-Risk (VaR). Using traditional parametric approaches based on GARCH and EGARCH to model the conditional volatility, we calculate univariate one-day ahead predictions of Value-at-Risk (VaR) under varying distributional assumptions. The accuracy of these predictions is then compared to that of a semiparametric approach, based on results from extreme value theory. For the 95% VaR, the EGARCH’s ability to incorporate the asymmetric behaviour of return volatility proves most useful. For higher quantiles, however, we show that what matters most for predictive accuracy is the underlying distributional assumption of the innovations, where the normal distribution falls behind other distributions which allow for thicker tails. Both the semiparametric approach and the conditional volatility models based on the t-distribution outperform the normal, especially at higher quantiles. As for the comparison between the semiparametric approach and the conditional volatility models with t-distributed innovations, the results are mixed. However, the evidence indicates that there certainly is a place for extreme value theory in financial risk management.

The peaks over threshold (POT) method provides an attractive framework for estimating the risk of extreme events such as severe storms or large insurance claims. However, the conventional POT procedure, where the threshold excesses are modelled by a generalized Pareto distribution, suffers from small samples and subjective threshold selection. In recent years, two alternative approaches have been proposed in the form of mixture models that estimate the threshold and a folding procedure that generates larger tail samples. In this paper the empirical performances of the conventional POT procedure, the folding procedure and a mixture model are compared by modelling data sets on fire insurance claims and hurricane damage costs. The results show that the folding procedure gives smaller standard errors of the parameter estimates and in some cases more stable quantile estimates than the conventional POT procedure. The mixture model estimates are dependent on the starting values in the numerical maximum likelihood estimation, and are therefore difficult to compare with those from the other procedures. The conclusion is that none of the procedures is overall better than the others but that there are situations where one method may be preferred.