Browsing by Author "Clark, Allan"

Now showing 1 - 17 of 17
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    Accurate estimation of risk when constructing efficient portfolios for the capital asset pricing model
    (2010) Zwane, Samkelo Sifiso; Clark, Allan; Troskie, Casper G
    In this paper, we investigate the behaviour of the efficient frontier and optimal portfolio of the Troskie-Hossain Capital Asset Pricing Model (TrosHos CAPM) and Sharpe Capital Asset Pricing Model (Sharpe CAPM) when the covariance structure of the residuals is correlated under the Markowitz formulation. By building in the dynamic time series models: AR, GARCH and AR/GARCH we were able to model the autocorrelation and heteroskedasticity of the residuals.
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    Application of the sequential t-test algorithm for analysing regime shifts to the southern Benguela ecosystem
    (2007) Howard, James A E; Moloney, Coleen; Jarre, Astrid; Clark, Allan
    Long-term ecosystem changes, such as regime shifts, have occurred in several marine ecosystems worldwide. Multivariate statistical methods have been used to detect such changes, but they have to date not been applied to the southern Benguela ecosystem. A weakness of many of the methods is that they require long time series data and do not provide robust results at the end of time series. A new method known as the sequential t-test algorithm for analysing regime shifts (STARS) is applied to a set of biological state variables and environmental and anthropogenic forcing variables in the southern Benguela.
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    Bayesian analysis of historical functional linear models with application to air pollution forecasting
    (2022) Junglee, Yovna; Erni, Birgit; Clark, Allan
    Historical functional linear models are used to analyse the relationship between a functional response and a functional predictor whereby only the past of the predictor process can affect the current outcome. In this work, we develop a Bayesian framework for the analysis of the historical functional linear model with multiple predictors. Different from existing Bayesian approaches to historical functional linear models, our proposed methodology is able to handle multiple functional covariates with measurement error and sparseness. The proposed model utilises the well-established connection between non-parametric smoothing and Bayesian methods to reduce sensitivity to the number of basis functions which are used to model the functional regression coefficients. We investigate two methods of estimation within the Bayesian framework. We first propose to smooth the functional predictors independently from the regression model in a two-stage analysis, and secondly, jointly with the regression model. The efficiency of the MCMC algorithms is increased by implementing a Cholesky decomposition to sample from high-dimensional Gaussian distributions and by taking advantage of the orthogonal properties of the functional principal components used to model the functional covariates. Our extensive simulation study shows substantial improvements in both the recovery of the functional regression surface and the true underlying functional response with higher coverage probabilities, when compared to a classical model under which the measurement error is unaccounted for. We further found that the Bayesian two-stage analysis outperforms the joint model under certain conditions. A major challenge with the collection of environmental data is that they are prone to measurement error, both random and systematic. Hence, our methodology provides a reliable functional data analytic framework for modelling environmental data. Our focus is on the application of our method to forecast the level of daily atmospheric pollutants using meteorological information such as hourly records of temperature, humidity and wind speed from data collected by the City of Cape Town, South Africa. The forecasts provided by the proposed Bayesian two-stage model are highly competitive against the functional autoregressive models which are traditionally used for functional time series.
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    Computational Psychiatry - Neuropsychological Bayesian reinforcement learning
    (2022) Wolpe, Zach; Shock, Jonathan; Cowley, Benjamin; Clark, Allan
    Cognitive science draws inspiration from a myriad of disciplines, and has become increasingly reliant on computational methods. In particular, theories of learning, operant conditioning and decision making have shown a natural synergy with statistical learning algorithms. This offers a unique opportunity to derive novel insight into the conditioning process by leveraging computational ideas. Specifically, ideas from Bayesian Inference and Reinforcement Learning. In this thesis, we examine the statistical properties of associative learning under uncertainty. We conducted a neuropsychological experiment on over 100 human subjects to measure a suite of executive functions. The primary experimental task (Card Sorting) gauges one's ability to learn, via inference, the structure of some latent pattern that drives the decision making process. We were able to successfully predict the subjects' behaviour in this task by fitting a Bayesian Reinforcement Learning model, alluding to the mechanics of the latent biological decision generating process and executive functions. Primarily, we detail the relationship between working memory capacity and associative learning.
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    Efficient Bayesian analysis of spatial occupancy models
    (University of Cape Town, 2020) Bleki, Zolisa; Clark, Allan
    Species conservation initiatives play an important role in ecological studies. Occupancy models have been a useful tool for ecologists to make inference about species distribution and occurrence. Bayesian methodology is a popular framework used to model the relationship between species and environmental variables. In this dissertation we develop a Gibbs sampling method using a logit link function in order to model posterior parameters of the single-season spatial occupancy model. We incorporate the widely used Intrinsic Conditional Autoregressive (ICAR) prior model to specify the spatial random effect in our sampler. We also develop OccuSpytial, a statistical package implementing our Gibbs sampler in the Python programming language. The aim of this study is to highlight the computational efficiency that can be obtained by employing several techniques, which include exploiting the sparsity of the precision matrix of the ICAR model and also making use of Polya-Gamma latent variables to obtain closed form expressions for the posterior conditional distributions of the parameters of interest. An algorithm for efficiently sampling from the posterior conditional distribution of the spatial random effects parameter is also developed and presented. To illustrate the sampler's performance a number of simulation experiments are considered, and the results are compared to those obtained by using a Gibbs sampler incorporating Restricted Spatial Regression (RSR) to specify the spatial random effect. Furthermore, we fit our model to the Helmeted guineafowl (Numida meleagris) dataset obtained from the 2nd South African Bird Atlas Project database in order to obtain a distribution map of the species. We compare our results with those obtained from the RSR variant of our sampler, those obtained by using the stocc statistical package (written using the R programming language), and those obtained from not specifying any spatial information about the sites in the data. It was found that using RSR to specify spatial random effects is both statistically and computationally more efficient that specifying them using ICAR. The OccuSpytial implementations of both ICAR and RSR Gibbs samplers has significantly less runtime compared to other implementations it was compared to.
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    Evaluating occupancy and the range dynamics of invasive bird species in South Africa
    (2022) Swingler, James; Distiller, Gregory; Clark, Allan
    There is great interest in the distribution of invasive species that threaten indigenous wildlife. All effective conservation management decisions need to be based on sound inference and predictions so that these species can be controlled and the risk posed to the local ecosystem minimized. Thus, there is significant benefit in the study of invasive species as a means of aiding those charged with protecting indigenous wildlife. The occupancy and population range dynamics of the Myna and Mallard species are individually investigated in the South African region by fitting static and dynamic occupancy models to a set of citizen science data for a 10-year study period between 2010-2019. The occupancy and detectability of the respective species is analysed using static occupancy models for the 2010 study season. The covariates included in the best fitting static models are used to estimate the initial occupancy and detection parameters for the dynamic models which now include estimates for colonization and local extinction. A sensitivity analysis pertaining to the dynamic models is implemented by altering the data structures in terms of the number of analysed sites and length of the detection histories. The results find the Myna's proximity to urban environments to play a significant role on its occupancy in 2010, and yearly changes in climatic and anthropogenic factors influence its 10-year range dynamics. The models fitted to the Mallard are inconclusive possibly due to the violation of the closure assumption potentially caused by migratory behaviour. The results are limited by the presence of a potentially migratory species when using a poorly designed study and highlights the difficulties of conducting an occupancy analysis on a highly mobile avian species as opposed to their sedentary counterpart. The workings of this dissertation support previous claims that an increase in the quantity of sites, and thus the degree of overlapping sites over the different seasons, will improve the precision of the model estimates. However, caution must be exercised when increasing the length of the seasonal detection histories and should generally be set to no more than 10 repeated visits to a site.
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    Human action recognition with 3D convolutional neural networks
    (2015) Cronje, Frans; Clark, Allan
    Convolutional neural networks (CNNs) adapt the regular fully-connected neural network (NN) algorithm to facilitate image classification. Recently, CNNs have been demonstrated to provide superior performance across numerous image classification databases including large natural images (Krizhevsky et al., 2012). Furthermore, CNNs are more readily transferable between different image classification problems when compared to common alternatives. The extension of CNNs to video classification is simple and the rationale behind the components of the model are still applicable due to the similarity between image and video data. Previous CNNs have demonstrated good performance upon video datasets, however have not employed methods that have been recently developed and attributed improvements in image classification networks. The purpose of this research to build a CNN model that includes recently developed elements to present a human action recognition model which is up-to-date with current trends in CNNs and current hardware. Focus is applied to ensemble models and methods such as the Dropout technique, developed by Hinton et al. (2012) to reduce overfitting, and learning rate adaptation techniques. The KTH human action dataset is used to assess the CNN model, which, as a widely used benchmark dataset, facilitates the comparison between previous work performed in the literature. Three CNNs are built and trained to provide insight into design choices as well as allow the construction of an ensemble model. The final ensemble model achieved comparative performance to previous CNNs trained upon the KTH data. While the inclusion of new methods to the CNN model did not result in an improvement on previous models, the competitive result provides an alternative combination of architecture and components to other CNN models.
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    Insurance recommendation engine using a combined collaborative filtering and neural network approach
    (2021) Pillay, Prinavan; Er, Sebnem; Clark, Allan
    A recommendation engine for insurance modelling was designed, implemented and tested using a neural network and collaborative filtering approach. The recommendation engine aims to suggest suitable insurance products for new or existing customers, based on their features or selection history. The collaborative filtering approach used matrix factorization on an existing user base to provide recommendation scores for new products to existing users. The content based method used a neural network architecture which utilized user features to provide a product recommendation for new users. Both methods were deployed using the Tensorflow machine learning framework. The hybrid approach helps solve for cold start problems where users have no interaction history. The accuracy on the collaborative filtering produced 0.13 root mean square error based on implicit feedback rating of 0-1, and an overall Top-3 classification accuracy (ability to predict one of the top 3 choices of a customer) of 83.8%. The neural network system achieved an accuracy of 77.2% on Top-3 classification. The system thus achieved good training performance and given further modifications, could be used in a production environment.
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    Loss distributions in consumer credit risk : macroeconomic models for expected and unexpected loss
    (2016) Malwandla, Musa; Rajaratnam, Kanshukan; Clark, Allan
    This thesis focuses on modelling the distributions of loss in consumer credit arrangements, both at an individual level and at a portfolio level, and how these might be influenced by loan-specific factors and economic factors. The thesis primarily aims to examine how these factors can be incorporated into a credit risk model through logistic regression models and threshold regression models. Considering the fact that the specification of a credit risk model is influenced by its purpose, the thesis considers the IFRS 7 and IFRS 9 accounting requirements for impairment disclosure as well as Basel II regulatory prescriptions for capital requirements. The thesis presents a critique of the unexpected loss calculation under Basel II by considering the different ways in which loans can correlate within a portfolio. Two distributions of portfolio losses are derived. The Vašíček distribution, which is the assumed in Basel II requirements, was originally derived for corporate loans and was never adapted for application in consumer credit. This makes it difficult to interpret and validate the correlation parameters prescribed under Basel II. The thesis re-derives the Vašíček distribution under a threshold regression model that is specific to consumer credit risk, thus providing a way to estimate the model parameters from observed experience. The thesis also discusses how, if the probability of default is modelled through logistic regression, the portfolio loss distribution can be modelled as a log-log-normal distribution.
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    Methods for analyzing cost effectiveness data from cluster randomized trials
    (BioMed Central Ltd, 2007) Bachmann, Max; Fairall, Lara; Clark, Allan; Mugford, Miranda
    BACKGROUND:Measurement of individuals' costs and outcomes in randomized trials allows uncertainty about cost effectiveness to be quantified. Uncertainty is expressed as probabilities that an intervention is cost effective, and confidence intervals of incremental cost effectiveness ratios. Randomizing clusters instead of individuals tends to increase uncertainty but such data are often analysed incorrectly in published studies. METHODS: We used data from a cluster randomized trial to demonstrate five appropriate analytic methods: 1) joint modeling of costs and effects with two-stage non-parametric bootstrap sampling of clusters then individuals, 2) joint modeling of costs and effects with Bayesian hierarchical models and 3) linear regression of net benefits at different willingness to pay levels using a) least squares regression with Huber-White robust adjustment of errors, b) a least squares hierarchical model and c) a Bayesian hierarchical model. RESULTS: All five methods produced similar results, with greater uncertainty than if cluster randomization was not accounted for. CONCLUSION: Cost effectiveness analyses alongside cluster randomized trials need to account for study design. Several theoretically coherent methods can be implemented with common statistical software.
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    Modelling non-linearity in 3D shapes: A comparative study of Gaussian process morphable models and variational autoencoders for 3D shape data
    (2021) Fehr, Fabio; Clark, Allan; Mutsvangwa, Tinashe
    The presence of non-linear shape variation in 3D data is known to influence the reliability of linear statistical shape models (SSM). This problem is regularly acknowledged, but disregarded, as it is assumed that linear models are able to adequately approximate such non-linearities. Model reliability is crucial for medical imaging and computer vision tasks; however, prior to modelling, the non-linearity in the data is not often considered. The study provides a framework to identify the presence of non-linearity in using principal component analysis (PCA) and autoencoders (AE) shape modelling methods. The data identified to have linear and non-linear shape variations is used to compare two sophisticated techniques: linear Gaussian process morphable models (GPMM) and non-linear variational autoencoders (VAE). Their model performance is measured using generalisation, specificity and computational efficiency in training. The research showed that, given limited computational power, GPMMs managed to achieve improved relative generalisation performance compared to VAEs, in the presence of non-linear shape variation by at least a factor of six. However, the non-linear VAEs, despite the simplistic training scheme, presented improved specificity generative performance of at least 18% for both datasets.
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    Optimising the Optimiser: Meta NeuroEvolution for Artificial Intelligence Problems
    (2021) Hayes, Max Nieuwoudt; Bassett, Bruce; Clark, Allan
    Since reinforcement learning algorithms have to fully solve a task in order to evaluate a set of hyperparameter values, conventional hyperparameter tuning methods can be highly sample inefficient and computationally expensive. Many widely used reinforcement learning architectures originate from scientific papers which include optimal hyperparameter values in the publications themselves, but do not indicate how the hyperparameter values were found. To address the issues related to hyperparameter tuning, three different experiments were investigated. In the first two experiments, Bayesian Optimisation and random search are compared. In the third and final experiment, the hyperparameter values found in second experiment are used to solve a more difficult reinforcement learning task, effectively performing hyperparameter transfer learning (later referred to as meta-transfer learning). The results from experiment 1 showed that there are certain scenarios in which Bayesian Optimisation outperforms random search for hyperparameter tuning, while the results of experiment 2 show that as more hyperparameters are simultaneously tuned, Bayesian Optimisation consistently finds better hyperparameter values than random search. However, BO took more than twice the amount of time to find these hyperparameter values than random search. Results from the third and final experiment indicate that hyperparameter values learned while tuning hyperparameters for a relatively easy to solve reinforcement learning task (Task A), can be used to solve a more complex task (Task B). With the available computing power for this thesis, hyperparameter optimisation was possible on the tasks in experiment 1 and experiment 2. This was not possible on the task in experiment 3, due to limited computing resources and the increased complexity of the reinforcement learning task in experiment 3, making the transfer of hyperparameters from one task (Task A) to the more difficult task (Task B) highly beneficial for solving the more computationally expensive task. The purpose of this work is to explore the effectiveness of Bayesian Optimisation as a hyperparameter tuning algorithm on the reinforcement learning algorithm NEAT's hyperparemters. An additional goal of this work is the experimental use of hyperparameter value transfer between reinforcement learning tasks, referred to in this work as Meta-Transfer Learning. This is introduced and discussed in greater detail in the Introduction chapter. All code used for this work is available in the repository: • https://github.com/maaxnaax/MSc_code
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    Quantitative models for prudential credit risk management
    (2021) Malwandla, Musa; Rajaratnam, Kanshukan; Clark, Allan
    The thesis investigates the exogenous maturity vintage model (EMV) as a framework for achieving unification in consumer credit risk analysis. We explore how the EMV model can be used in origination modelling, impairment analysis, capital analysis, stress-testing and in the assessment of economic value. The thesis is segmented into five themes. The first theme addresses some of the theoretical challenges of the standard EMV model – namely, the identifiability problem and the forecasting of the components of the model in predictive applications. We extend the model beyond the three time dimensions by introducing a behavioural dimension. This allows the model to produce loan-specific estimates of default risk. By replacing the vintage component with either an application risk or a behavioural risk dimension, the model resolves the identifiability problem inherent in the standard model. We show that the same model can be used interchangeably to produce a point-in-time probability forecast, by fitting a time series regression for the exogenous component, and a through-the-cycle probability forecast, by omitting the exogenous component. We investigate the use of the model for regulatory capital and stress-testing under Basel III, as well as impairment provisioning under IFRS 9. We show that when a Gaussian link function is used the portfolio loss follows a Vašíček distribution. Furthermore, the asset correlation coefficient (as defined under Basel III) is shown to be a function of the level of systemic risk (which is measured by the variance of the exogenous component) and the extent to which the systemic risk can be modelled (which is measured by the coefficient of determination of the regression model for the exogenous component). The second theme addresses the problem of deriving a portfolio loss distribution from a loan-level model for loss. In most models (including the Basel-Vašíček regimes), this is done by assuming that the portfolio is infinitely large – resulting in a loss distribution that ignores diversifiable risk. We thus show that, holding all risk parameters constant, this assumption leads to an understatement of the level of risk within a portfolio – particularly for small portfolios. To overcome this weakness, we derive formulae that can be used to partition the portfolio risk into risk that is diversifiable and risk that is systemic. Using these formulae, we derive a loss distribution that better-represents losses under portfolios of all sizes. The third theme is concerned with two separate issues: (a) the problem of model selection in credit risk and (b) the problem of how to accurately measure probability of insolvency in a credit portfolio. To address the first problem, we use the EMV model to study the theoretical properties of the Gini statistic for default risk in a portfolio of loans and derive a formula that estimates the Gini statistic directly from the model parameters. We then show that the formulae derived to estimate the Gini statistic can be used to study the probability of insolvency. To do this, we first show that when capital requirements are determined to target a specific probability of solvency on a through-the-cycle basis, the point-in-time probability of insolvency can be considerably different from the through-the-cycle probability of insolvency – thus posing a challenge from a risk management perspective. We show that the extent of this challenge will be greater for more cyclical loan portfolios. We then show that the formula derived for the Gini statistic can be used to measure the extent of the point-in-time insolvency risk posed by using a through-the-cycle capital regime. The fourth theme considers the problem of survival modelling with time varying covariates. We propose an extension to the Cox regression model, allowing the inclusion of time-varying macroeconomic variables as covariates. The model is specifically applied to estimate the probability of default in a loan portfolio, where the experience is decomposed the experience into three dimensions: (a) a survival time dimension; (b) a behavioural risk dimension; and (c) calendar time dimension. In this regard, the model can also be viewed as an extension of the EMV model – adding a survival time dimension. A model is built for each dimension: (a) the survival time dimension is modelled by a baseline hazard curve; (b) the behavioural risk dimension is modelled by a behavioural risk index; and (c) the calendar time dimension is modelled by a macroeconomic risk index. The model lends itself to application in modelling probability of default under the IFRS 9 regime, where it can produce estimates of probability of default over variable time horizons, while accounting for time-varying macroeconomic variables. However, the model also has a broader scope of application beyond the domains of credit risk and banking. In the fifth and final theme, we introduce the concept of embedded value to a banking context. In longterm insurance, embedded value relates to the expected economic value (to shareholders) of a book of insurance contracts and is used for appraising insurance companies and measuring management's performance. We derive formulae for estimating the embedded value of a portfolio of loans, which we show to be a function of: (a) the spread between the rate charged to the borrower and the cost of funding; (b) the tenure of the loan; and (c) the level of credit risk inherent in the loan. We also show how economic value can be attributed between profits from maturity transformation and profits from credit and liquidity margin. We derive formulae that can be used to analyse the change in embedded value throughout the life of a loan. By modelling the credit loss component of embedded value, we derive a distribution for the economic value of a book of business. The literary contributions made by the thesis are of practical significance. The thesis offers a way for banks and regulators to accurately estimate the value of the asset correlation coefficient in a manner that controls for portfolio size and intertemporal heterogeneity. This will lead to improved precision in determining capital adequacy – particularly for institutions operating in uncertain environments and those operating small credit portfolios – ultimately enhancing the integrity of the financial system. The thesis also offers tools to help bank management appraise the financial performance of their businesses and measure the value created for shareholders.
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    Quantitative Models for Prudential Credit Risk Management
    (2021) Malwandla, Musa; Rajaratnam, Kanshukan; Clark, Allan
    The thesis investigates the exogenous maturity vintage model (EMV) as a framework for achieving unification in consumer credit risk analysis. We explore how the EMV model can be used in origination modelling, impairment analysis, capital analysis, stress-testing and in the assessment of economic value. The thesis is segmented into five themes. The first theme addresses some of the theoretical challenges of the standard EMV model – namely, the identifiability problem and the forecasting of the components of the model in predictive applications. We extend the model beyond the three time dimensions by introducing a behavioural dimension. This allows the model to produce loan-specific estimates of default risk. By replacing the vintage component with either an application risk or a behavioural risk dimension, the model resolves the identifiability problem inherent in the standard model. We show that the same model can be used interchangeably to produce a point-in-time probability forecast, by fitting a time series regression for the exogenous component, and a through-the-cycle probability forecast, by omitting the exogenous component. We investigate the use of the model for regulatory capital and stress-testing under Basel III, as well as impairment provisioning under IFRS 9. We show that when a Gaussian link function is used the portfolio loss follows a Vašíček distribution. Furthermore, the asset correlation coefficient (as defined under Basel III) is shown to be a function of the level of systemic risk (which is measured by the variance of the exogenous component) and the extent to which the systemic risk can be modelled (which is measured by the coefficient of determination of the regression model for the exogenous component). The second theme addresses the problem of deriving a portfolio loss distribution from a loan-level model for loss. In most models (including the Basel-Vašíček regimes), this is done by assuming that the portfolio is infinitely large – resulting in a loss distribution that ignores diversifiable risk. We thus show that, holding all risk parameters constant, this assumption leads to an understatement of the level of risk within a portfolio – particularly for small portfolios. To overcome this weakness, we derive formulae that can be used to partition the portfolio risk into risk that is diversifiable and risk that is systemic. Using these formulae, we derive a loss distribution that better-represents losses under portfolios of all sizes. The third theme is concerned with two separate issues: (a) the problem of model selection in credit risk and (b) the problem of how to accurately measure probability of insolvency in a credit portfolio. To address the first problem, we use the EMV model to study the theoretical properties of the Gini statistic for default risk in a portfolio of loans and derive a formula that estimates the Gini statistic directly from the model parameters. We then show that the formulae derived to estimate the Gini statistic can be used to study the probability of insolvency. To do this, we first show that when capital requirements are determined to target a specific probability of solvency on a through-the-cycle basis, the point-in-time probability of insolvency can be considerably different from the through-the-cycle probability of insolvency – thus posing a challenge from a risk management perspective. We show that the extent of this challenge will be greater for more cyclical loan portfolios. We then show that the formula derived for the Gini statistic can be used to measure the extent of the point-in-time insolvency risk posed by using a through-the-cycle capital regime. The fourth theme considers the problem of survival modelling with time varying covariates. We propose an extension to the Cox regression model, allowing the inclusion of time-varying macroeconomic variables as covariates. The model is specifically applied to estimate the probability of default in a loan portfolio, where the experience is decomposed the experience into three dimensions: (a) a survival time dimension; (b) a behavioural risk dimension; and (c) calendar time dimension. In this regard, the model can also be viewed as an extension of the EMV model – adding a survival time dimension. A model is built for each dimension: (a) the survival time dimension is modelled by a baseline hazard curve; (b) the behavioural risk dimension is modelled by a behavioural risk index; and (c) the calendar time dimension is modelled by a macroeconomic risk index. The model lends itself to application in modelling probability of default under the IFRS 9 regime, where it can produce estimates of probability of default over variable time horizons, while accounting for time-varying macroeconomic variables. However, the model also has a broader scope of application beyond the domains of credit risk and banking. In the fifth and final theme, we introduce the concept of embedded value to a banking context. In longterm insurance, embedded value relates to the expected economic value (to shareholders) of a book of insurance contracts and is used for appraising insurance companies and measuring management's performance. We derive formulae for estimating the embedded value of a portfolio of loans, which we show to be a function of: (a) the spread between the rate charged to the borrower and the cost of funding; (b) the tenure of the loan; and (c) the level of credit risk inherent in the loan. We also show how economic value can be attributed between profits from maturity transformation and profits from credit and liquidity margin. We derive formulae that can be used to analyse the change in embedded value throughout the life of a loan. By modelling the credit loss component of embedded value, we derive a distribution for the economic value of a book of business. The literary contributions made by the thesis are of practical significance. The thesis offers a way for banks and regulators to accurately estimate the value of the asset correlation coefficient in a manner that controls for portfolio size and intertemporal heterogeneity. This will lead to improved precision in determining capital adequacy – particularly for institutions operating in uncertain environments and those operating small credit portfolios – ultimately enhancing the integrity of the financial system. The thesis also offers tools to help bank management appraise the financial performance of their businesses and measure the value created for shareholders.
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    The impact of estimation frequency on Value at Risk (VaR) and Expected Shortfall (ES) forecasts: an empirical study on conditional extreme value models
    (2020) Coyne, Alice Elizabeth; Clark, Allan
    This study investigates extreme market events which occur in the tails of a distribution. The extreme events occur with a very low probability, but with significant consequences, which is what makes them of interest. In this study 20 years of data from both the S&P 500 and the JSE All Share index have been used. An extreme value approach has been taken to quantify the risks associated with extreme market events. To achieve this a two phased process is used to calculated the Value at Risk and Expected Shortfall. The first phase involved running the daily returns through the GARCH model, and then extracting the residuals. The second phase involves using the Block Maxima Method, or Peaks over Threshold method to fit the residuals to the Generalized Extreme Value Distribution or the Generalized Pareto Distribution. Finally, the impact of estimation frequency is considered for each of the models. In conclusion, taking an extreme value approach to provide a statistically sound method to calculate risk, even when the parameters of the model are updated less frequently, this is preferable to simpler models where the parameter estimates are updated daily.
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    Using Neural Networks to identify Individual Animals from Photographs
    (2019) Kabuga, Emmanuel; Durbach, Ian; Bah, Bubacarr; Clark, Allan
    Effective management needs to know sizes of animal populations. This can be accomplished in various ways, but a very popular way is mark-recapture studies. Mark-recapture studies need a way of telling if a captured animal has been previously seen. For traditional mark-recapture, this is achieved by applying a tag to the animal. For non-invasive mark-recapture methods which exploit photographs, there is no tag on the animal’s body. As a result, these methods require animals to be individually identifiable. They assess if an animal has been caught before by examining photographs for animals which have individual-specific marks (Cross et al., 2014; Gomez et al., 2016; Beijbom et al., 2016; Körschens, Barz, and Denzler, 2018). This study develops a model which can reliably match photographs of the same individual based on individual-specific marks. The model consists of two main parts, an object detection model, and a classifier which takes two photos as input and outputs a predicted probability that the pair is from the same individual (a match). The object detection model is a convolutional neural network (CNN) and the matching classifier is a special kind of CNN called a siamese network. The siamese network uses a pair of CNNs that share weights to summarise the images, followed by some dense layers which combine the summaries into measures of similarity which can be used to predict a match. The model is tested on two case studies, humpback whales (HBWs) and western leopard toads (WLTs). The HBW dataset consists of images originally collected by various institutions across the globe and uploaded to the Happywhale platform which encourages scientists to identify individual mammals. HBWs can be identified by their fins and specials markings. There is lots of data for this problem. The WLT dataset consists of images collected by citizen scientists in South Africa. They were either uploaded to iSpot, a citizen science project which collects images or sent to the (WLT) project, a conservation project staffed by volunteers. WLTs can be identified by their unique spots. There is a little data for this problem. One part of this dataset consists of labelled individuals and another part is unlabelled. The model was able to give good results for both HBWs and WLTs. In 95% of the cases the model managed to correctly identify if a pair of images is from the same HBW individual or not. It accurately identified if a pair of images is drawn from the same WLT individual or not in 87% of the cases. This study also assessed the effectiveness of the semi-supervised approach on the WLT unlabelled dataset. In this study, the semisupervised approach has been partially successful. The model was able to identify new individuals and matches which were not identified before, but they were relatively few in numbers. Without an exhaustive check of the data, it is not clear whether this is due to the failure of the semi-supervised approach, or because there are not many matches in the data. After adding the newly identified and labelled individuals to the WLT labelled dataset, the model slightly improved its performance and correctly identified 89% of WLT pairs. A number of computer-aided photo-matching algorithms have been proposed (Matthé et al., 2017). This study also assessed the performance of Wild-ID (Bolger et al., 2012), one of the commonly used photo-matching algorithm on both HBW and WLT datasets. The model developed in this thesis achieved very competitive results compared with Wild-ID. Model accuracies for the proposed siamese network were much higher than those returned by Wild-ID on the HBW dataset, and roughly the same on the WLT dataset.
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    Volatility forecasting using Double-Markov switching GARCH models under skewed Student-t distribution
    (2012) Mazviona, Batsirai Winmore; Clark, Allan
    This thesis focuses on forecasting the volatility of daily returns using a double Markov switching GARCH model with a skewed Student-t error distribution. The model was applied to individual shares obtained from the Johannesburg Stock Exchange (JSE). The Bayesian approach which uses Markov Chain Monte Carlo was used to estimate the unknown parameters in the model. The double Markov switching GARCH model was compared to a GARCH(1,1) model. Value at risk thresholds and violations ratios were computed leading to the ranking of the GARCH and double Markov switching GARCH models. The results showed that double Markov switching GARCH model performs similarly to the GARCH model based on the ranking technique employed in this thesis.