Department of Mathematical and Computational Sciences
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Browsing Department of Mathematical and Computational Sciences by Author "Bere, Aphonce"
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Item Open Access Forecasting wavelet denoised global horizontal irradiance using attention-based long short term memory network: A case study of South Africa(2022-07-15) Nelwamondo, Ndamulelo Innocent; Sigauke, Caston; Bere, Aphonce; Thanyani, MaduvhahafaniMicrogrids are becoming a crucial component of the electricity grid in dependability, economics, and environmental sustainability. Microgrids rely heavily on renewable energy sources. From an engineering standpoint, anticipating short-term solar generation is a critical challenge in microgrid planning and design. Anticipating solar power is heavily reliant on forecasting sun radiation. Short-term solar radiation forecasting may also be used to estimate the energy potentials of photovoltaic (PV) panels impacted by degradation rates. A comparison of multiple models, namely the Autoregressive Integrated Moving Average (ARIMA), Long Short Term Memory (LSTM), Attention-based LSTM and a hybrid Attention-based LSTM-ARIMA for forecasting 5-day ahead 1-minute solar radiation is performed in this study. The best model for forecasting Global Solar Radiation(GHI) from Richtersveld station is ARIMA with MAE = 0.782 and RMSE = 1.271, followed by hybrid model with MAE = 4.120 and RMSE = 4.987. For Stellenbosch University station, attention LSTM was the best with MAE = 1.512 and RMSE = 1.640, followed by hybrid with MAE = 2.011 and RMSE = 2.511. The hybrid attention-based LSTM-ARIMA model on the USAid Venda station was the best fitting model with RMSE = 7.383 and MAE = 14.1293, followed by LSTM with MAE = 7.817 and RMSE = 8.444. Comparing the results on nonwavelet denoised and wavelet denoised, models performed better on wavelet denoised data. ARIMA model was the best with MAE = 0.194 and RMSE = 0.542, followed by hybrid with MAE = 2.176 and RMSE = 2.308.Item Open Access Modelling equity risk and external dependence: A survey of four African Stock Markets(2019-05-18) Samuel, Richard Abayomi; Sigauke, Caston; Bere, AphonceThe ripple e ect of a stock market crash due to extremal dependence is a global issue with key attention and it is at the core of all modelling e orts in risk management. Two methods of extreme value theory (EVT) were used in this study to model equity risk and extremal dependence in the tails of stock market indices from four African emerging markets: South Africa, Nigeria, Kenya and Egypt. The rst is the \bivariate-threshold-excess model" and the second is the \point process approach". With regards to the univariate analysis, the rst nding in the study shows in descending hierarchy that volatility with persistence is highest in the South African market, followed by Egyptian market, then Nigerian market and lastly, the Kenyan equity market. In terms of risk hierarchy, the Egyptian EGX 30 market is the most risk-prone, followed by the South African JSE-ALSI market, then the Nigerian NIGALSH market and the least risky is the Kenyan NSE 20 market. It is therefore concluded that risk is not a brainchild of volatility in these markets. For the bivariate modelling, the extremal dependence ndings indicate that the African continent regional equity markets present a huge investment platform for investors and traders, and o er tremendous opportunity for portfolio diversi cation and investment synergies between markets. These synergistic opportunities are due to the markets being asymptotic (extremal) independent or (very) weak asymptotic dependent and negatively dependent. This outcome is consistent with the ndings of Alagidede (2008) who analysed these same markets using co-integration analysis. The bivariate-threshold-excess and point process models are appropriate for modelling the markets' risks. For modelling the extremal dependence however, given the same marginal threshold quantile, the point process has more access to the extreme observations due to its wider sphere of coverage than the bivariate-threshold-excess model.