Masters Degrees (Statistics and Actuarial Science)

Permanent URI for this collection

https://scholar.sun.ac.za/handle/10019.1/733

Browse

Browsing Masters Degrees (Statistics and Actuarial Science) by browse.metadata.advisor "Kamper, Francois"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Discriminant analysis using sparse graphical models
    (Stellenbosch : Stellenbosch University, 2020-03) Botha, Dylon; Kamper, Francois; Bierman, Surette; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY : The objective of this thesis is the proposal of a new classification method. This classification method is an extension of classical quadratic discriminant analysis (QDA), where the focus is placed on relaxing the assumption of normality, and on overcoming the adverse effect of the large number of parameters that needs to be estimated when applying QDA. To relax the assumption of normality, we consider assigning to each class density a different nonparanormal distribution. Based on these nonparanormal distributions, new discriminant functions can be derived. When one considers the use of a nonparanormal distribution, the underlying assumption is that the associated random vector, can through the use of an appropriate transformation, be made to follow a Gaussian distribution. Such a transformation is based on the marginals of the distribution, which is to be estimated in a nonparametric way. The large number of parameters in QDA is a result of the estimation of class precision matrices. To overcome this problem, penalised maximum likelihood estimation is performed by placing an L1 penalty on the size of the elements in the class precision matrices. This leads to sparse precision matrix estimates, and therefore also to a reduction in the number of estimated parameters. Combining the above approaches to overcome the problems induced by nonnormality and a large number of parameters to estimate, leads to the following novel classification method. To each class density, a separate transformation is applied. Thereafter L1 penalised maximum likelihood estimation is performed in the transformed space. The resulting parameter estimates are then plugged into the nonparanormal discriminant functions, thereby facilitating classification. An empirical evaluation of the novel proposal shows it to be competitive with a wide array of existing classifiers. We also establish a connection to probabilistic graphical models, which could aid in the interpretation of this new technique.
  • Thumbnail Image
    Item
    Short-term wind speed prediction using various forecasting methods
    (Stellenbosch : Stellenbosch University, 2020-03) Nambandi, Maria Ndinelago; Kamper, Francois; Stellenbosch University. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    ENGLISH SUMMARY : There is a significant challenge in finding ways to enhance energy security and decrease greenhouse gas emissions emanating from the consumption of non-renewable resources for energy. The release of greenhouse gases causes global warming and is considered not clean. Compared to current conventional sources of energy, such as fossil resources, renewable energy sources have become more attractive for electricity production as it has been identified as clean with a closed carbon dioxide cycle. Thus, the CO2 produced during processing is reabsorbed by plants for food production. A significant development in the electricity industry in recent years has been the fast growth of wind power. The wind power generated from the wind depends on meteorological conditions such as wind speed and wind direction. These meteorological conditions are considered stochastic in nature, especially wind speed, and attempts to accurately forecast future values are therefore considered important in power generation. There are various studies in the literature which make use of statistical techniques to predict wind speed data. In this thesis, the short-term prediction of hourly wind speeds at 60m hub height for two sites, Jozini and Memel in South Africa, over a 1 to 24-hour forecast horizon is considered. The potential short-term wind speed at a site was predicted using statistical forecasting techniques such as traditional time series models (ARMA, ARIMA, seasonal ARIMA and regression using Fourier terms with ARMA errors), multilayer perceptron (MLP) neural networks and long short term memory (LSTM) recurrent neural networks. These predictions are relevant for planning purposes to ensure that the necessary base load on the electricity grid is established at all times. All forecasting techniques were applied to forecast wind speeds for each forecast horizon and site. Different LSTM and MLP configurations were created using a different number of hidden layers, a different number of hidden nodes in each layer, different learning rates, and different activation functions. The forecast performances of each configuration were compared to the persistence forecast (benchmark model). Root mean square errors (RMSE) and mean absolute percentage errors (MAPE) were used to select the configuration that best predicted the test data. Our empirical results show that the three different statistical techniques considered achieved similar results for each site and all the forecast horizons. Seasonal ARIMA models were used because there was a clear indication that the wind speeds data for Jozini and Memel are seasonal, with daily and annual regular cycles respectively. For the Memel site, a more accurate model was obtained through the use of regression with ARMA errors, where the Fourier term corresponding to annual seasonality was used as a regressor. Overall, the persistence forecast was the least accurate model to predict wind speeds at 60m height for all sites. LSTM configurations and regression using Fourier terms with ARMA errors achieved similar results with a slight improvement for the latter. Neural networks achieved comparable results with traditional time series models, thus, suggesting that the behaviour of wind speeds for each site is not overly complicated and simple forecasting techniques can be used for modelling. The predicted values obtained using the most accurate model, and the actual values for each site were plotted. The results showed that regression with Fourier terms and ARMA errors method could accurately predict the oscillations of the wind speed series with high accuracy, and it predicted most of the sudden peaks in the series. The analysis reported in this work provides much insight into wind speed forecasting for researchers who might apply statistical forecasting techniques on wind data in the future.