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Estimating the size of the underground economy in South Africa using the Multiple Indicators Multiple Cause Model (MIMIC) and the Currency Demand Approach (CDA).
(2021) Koloane, Cathrine Thato.; Bodhlyera, Oliver.
The underground economy is a major challenge across the world affecting both developed and developing economies. South Africa is no exception to this phenomenon and has lost billions of rands due to the underground economy. Tax revenue loss due to illicit trade was estimated to be approximately R36.5 billion in 2019, with illicit cigarettes and tobacco and undervalued clothing and textiles perceived to be the main contributors to this economy. The objective of this research is to estimate the size of the underground economy in South Africa using the Currency Demand Approach (CDA) and the Multiple Indicators Multiple Cause (MIMIC) models. To accomplish this, secondary economic data was obtained from Statistics South Africa (STATSSA), World Bank, South African Reserve Bank (SARB) and the International Monetary Fund (IMF) for the period 2000 to 2020. The results from the MIMIC model showed that the underground economy in South Africa was growing with estimates ranging from 25.4% to 32.3% of GDP for 2003 to 2020.The model further indicated that mining employment rate, tax burden and government expenditure are the causes of the underground economy and Nominal Gross Domestic Product (NGDP) and labour force participation rate are the indicators of the underground economy. Similarly, the CDA model showed a steadily increasing underground economy estimated at 28.8% of GDP on average for 2003 to 2020. Furthermore, the CDA model showed that NGDP, tax burden, interest rate, unemployment rate, self-employment rate and social benefits granted by the government are determinants of the underground economy. This study makes a significant contribution to the body of knowledge in this research area and will provide much needed insights on the relative magnitude of the underground economy, drivers of the underground economy and the extent of tax evasion in South Africa, ultimately contributing towards an improved tax base and compliance. It will further serve as a basis for future research in this topic by academia, private sector, government, multilateral bodies and all other interest groups.
Forecasting electricity demand using univariate time series volatility forecasting models : a case study of Uganda and South Africa.
(2016) Nakiyingi, Winnie.; Bodhlyera, Oliver.; Mwambi, Henry Godwell.
Different sectors of economies are significantly affected by the supply of electricity. However, with the available limited resources, supply and demand of electricity in Africa are strongly correlated. In order to efficiently improve electricity supply, its demand has to be accurately predicted. In this research, we analyse electricity demand in two cases; peak monthly electricity demand in Uganda from January 2008 to December 2013, and daily electricity demand for South Africa from 1st January 2004 to 30th June 2008, using ARIMA and ARCH/GARCH models. We use this data to forecast future demand for both countries in order to help policy makers in the electricity sector make decisions for sustainable development of both countries. GARCH models are introduced to correct the volatility found in South Africa's daily demand data. Results from the study show that; for Uganda, a seasonal ARIMA(0,0,0)(1,1,1)[12] model describes the data better, with RMSE of 4.872027 and MAPE of 2.347028, and gives better forecasts which display a continued increase in electricity demand for months ahead. For South African data, a seasonal ARIMA(1,0,1)(0,1,0)[365] describes the data better but a standard GARCH(1,1) with normally distributed error terms accommodates volatility. Therefore, a combination of the two models produces better forecast accuracy.
Integrating artificial neural networks, simulation and optimisation techniques in improving public emergency ambulance preparedness for heterogeneous regions under stochastic environments.
(2021) Mapuwei, Tichaona Wilbert.; Bodhlyera, Oliver.; Mwambi, Henry Godwell.
The Bulawayo Emergency Medical Services (BEMS) department continues to rely on judgemental methods with limited use of historical data for future predictions, strategic, tactical and operational level decision making. The rural to urban migration trend has seen the sprouting of new residential areas, and this has put pressure to the limited health, housing and education resources. It is expected that as population increases, there is subsequent increase in demand for public emergency services. However, public emergency ambulance demand trends has been decreasing in Bulawayo over the years. This trend is a sign of limited capacity of the service rather than demand itself. The situation demanded for consolidated efforts across all sectors including research, to restore confidence among residents, reduce health risk and loss of lives. The key objective was to develop a framework that would assist in integrating forecasting, simulation and optimisation techniques for ambulance deployment to predefined locations with heterogeneous demand patterns under stochastic environments, using multiple performance indicators. Secondary data from the Bulawayo Municipality archives from 2010 to 2018 was used for model building and validation. A combination of methods based on mathematics, statistics, operations research and computer science were used for data analysis, model building, sensitivity analysis and numerical experiments. Results indicate that feed forward neural network (FFNN) models are superior to traditional SARIMA models in predicting ambulance demand, over a short-term forecasting horizon. The FFNN model is more inclined to value estimation as compared to SARIMA model, which is directional as depicted by the linear pattern over time. An ANN model with a 7-(4)-1 architecture was selected to forecast 2019 public emergency ambulance demand (PEAD). Peak PEAD is expected in January, March, September and December whilst lower demand is expected for April, June and July 2019. Simulation models developed mimicked the prevailing levels of service for BEMS with six(6) operational ambulances. However. the average response times were well above 15 minutes, with significantly high average queuing times and number of ambulances queuing for service. These performance outcomes were highly undesirable as they pose a great threat to human based outcomes of safety and satisfaction with regards to service delivery. Optimisation for simulation was conducted by simultaneously minimising the average response time and average queuing time, while maximising throughput ratios. Increasing the number of ambulances influenced the average response time below a certain threshold, beyond this threshold, the average response time remained constant rather than decreasing gradually. Ambulance utilisation inversely varied to increase in the feet size. Numerical experiments revealed that reducing the response time results in the reduction in number of ambulances required for optimal ambulance deployment. It is imperative to simultaneously consider multiple performance indicators in ambulance deployment as it balances resource allocation and capacity utilisation, while avoiding idleness of essential equipment and human resources. Management should lobby for de-congestion and resurfacing of old and dilapidated roads to increase access and speed when responding to emergency calls. Future research should investigate the influence of varying service time on optimum deployment plans and consider operational costs, wages and other budgetary constraints that influence the allocation of critical but scarce resources such as personnel, equipment and emergency ambulance response vehicles.
Modelling and forecasting the costs of attending to electricity faults using univariate and multivariate time series forecasting models.
(2018) Buthelezi, Nkosiyapha Mthunzi.; Bodhlyera, Oliver.
Electricity price forecasting has turned into a very essential element for both public and private decision making. Both shortage of supply of electricity and electricity cost still remains the country’s most biggest problems and needs to be addressed decisively. Apart from the demand and supply side of electricity, electricity cost is an important part of electricity delivery. Therefore, the accurate estimation of electricity cost and it’s maintenance is an important part of the country’s electricity supply strategy. The main aim of this study is to forecast the cost of rectifying or attending to electricity faults. The study demonstrates that the AutoRegressive Integrated Moving Average (ARIMA), AutoRegressive Integrated Moving Average with exogenous variables (ARIMAX), Vector AutoRegressive (VAR) and Random Forest methods are capable of producing accurate forecasts of costs associated with attending to reported faults. In this study, we analyse the costs of attending to electrical faults in the Bethlehem and Bloemfontein areas of the Free State region of South Africa, from 4 January 2012 to 3 June 2017, using univariate and multivariate ARIMA, ARIMAX, VAR and Random Forest models. ARCH and GARCH models are also used to model the volatility found in the daily costs data. The model developed based on these data can be used to forecast future faults costs and can help policy makers with planning decisions.
Modelling South African official gold reserves position, and foreign exchange reserves position using time series models.
(2020) Gumede, Sibusiso.; Bodhlyera, Oliver.; Mwambi, Henry Godwell.
Every central bank of the country should hold enough reserves such as foreign exchange currency, gold, or any form of reserves to be able to help its country in times of difficulties or financial crises. This involves the process of ensuring that adequate official public sector foreign assets are readily available to meet any defined range of objectives by a country. Reserves can also play a pivotal role in supporting and maintaining confidence in the policies for monetary and exchange rate management, including the ability to intervene in the foreign market to influence the value of the local currency. It can also be used to provide proof to the market that a country can meet its current and future external obligations, limit external exposure by maintaining foreign currency liquidity to absorb shock during times of crisis, show the support of domestic currency by external assets, assist the government in meeting its foreign exchange needs and external debt obligations, and maintain sufficient reserves for national disasters or emergencies. All this cannot be done without the understanding of all factors that affect reserves of the country, hence careful analysis of reserves in a country plays a crucial role on how the central bank should manage the reserves of such a country. This includes a wide range of social, economic, and statistical analyses. However, this study focuses more on the statistical analysis part, which is, building models to predict or forecast the trajectory of reserves positions in future. These models should be able to consider all the factors that influence the reserves, such as trend, seasonality and the variability (random variability). The Seasonal ARIMA models were used as initial models to forecast the future reserves positions. Seasonal ARIMA Generalized Autoregressive Conditional Heteroskedasticity models with Skewed Student-t Distribution (SARIMA – GARCH – SSTD) were also used to forecast volatility from the foreign exchange reserves data after statistical test were carried out and the data was found to have ARCH Effects. The best volatility model that was found to produces best forecast for foreign exchange reserves data was the SARIMA (0,1,0) (2,1,0)12 – GARCH (1,1) – SSTD model. The SARIMA model developed earlier for gold reserves data was then benchmarked with the Holt-Winters' Seasonal method. The results from the analysis showed that SARIMA model outperformed Holt-Winters' Seasonal method in forecasting gold reserves positions. We found that future gold reserves positions can be better predicted using the SARIMA (1,1,0) (0,1,2)12 model. The best model was selected from many other models using model diagnostics process such as comparisons of the AIC, RMSE, number of significant parameters and the evaluation of residuals to identify their flexibility. Using the forecasting methods developed in this study, the central bank can better understand what to expect in the future and decide on what measures to implement for national economic stability.
A statistical analysis of dissolving timber pulp properties using linear mixed models.
(2017) Bodhlyera, Oliver.; Zewotir, Temesgen Tenaw.; Ramroop, Shaun.
The main focus of the study was to understand the behaviour of seven timber genotypes based on seven chemical properties observed during the chemical pulping process with the prime objective of developing methods of grouping different timber genotypes into compatible groups of timber that can be optimally processed together. Four related statistical methods were used in analysing the data and each had a specific objective. The random coefficients model was used to investigate how the genotypes evolve over the processing stages and it was discovered that the rates of change of the chemical properties studied depended on their initial readings at the beginning of processing. This trend applied for all seven genotypes of pulping trees studied. The important results that came out of fitting the random coefficient model to the data is that the higher the raw stage readings (initial values) the higher the rates of change in the chemical properties over the processing stages. The changes were either increases or decreases in the chemical property studied. The random coefficient model was also used to suggest a rudimental mixing index for the different genotypes based on the average ranking of their slope parameters (rates of change) for the seven variables studied. It was found, for example, that the genotypes GUA and GUW are the least mixable ones. Piecewise linear regression models were used to identify important variables when classifying genotypes and it was generally found that viscosity is not a very useful variable in the classification of genotypes. Using piecewise linear regression models together with kernel density estimation a mixing index (scale) was developed that can be used to determine which genotypes are the most mixable for chemical processing. A coparison of the random coefficient and the piecewise linear regression models shows that the two models yielded very similar conclusions on what genotypes are most mixable during processing. Joint modelling was used to analysis the correlations between evolutions of different chemical properties studied. The various levels of correlations between these variables were discussed. The main limitation of the joint modelling method was its computational challenges because of the many parameters that need to be estimated at the same time.
Time series analyses of microbiological counts associated with treated water quality data from Umgeni Water.
(2017) Lephoto, Thabo.; Bodhlyera, Oliver.; Mwambi, Henry Godwell.
Abstract available in PDF file.

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