Robust modelling framework for short-term forecasting of global horizontal irradiance

The increasing demand for electricity and the need for clean energy sources have increased solar energy use. Accurate forecasts of solar energy are required for easy management of the grid. This paper compares the accuracy of two Gaussian Process Regression (GPR) models combined with Additive Quantile Regression (AQR) and Bayesian Structural Time Series (BSTS) models in the 2-day ahead forecasting of global horizontal irradiance using data from the University of Pretoria from July 2020 to August 2021. Four methods were adopted for variable selection, Lasso, ElasticNet, Boruta, and GBR (Gradient Boosting Regression). The variables selected using GBR were used because they produced the lowest MAE (Minimum Absolute Errors) value. A comparison of seven models GPR (Gaussian Process Regression), Two-layer DGPR (Two-layer Deep Gaussian Process Regression), bstslong (Bayesian Structural Time Series long), AQRA (Additive Quantile Regression Averaging), QRNN(Quantile Regression Neural Network), PLAQR(Partial Linear additive Quantile Regression), and Opera(Online Prediction by ExpRt Aggregation) was made. The evaluation metrics used to select the best model were the MAE (Mean Absolute Error) and RMSE (Root Mean Square Error). Further evaluations were done using proper scoring rules and Murphy diagrams. The best individual model was found to be the GPR. The best forecast combination was AQRA ((AQR Averaging) based on MAE. However, based on RMSE, GPNN was the best forecast combination method. Companies such as Eskom could use the methods adopted in this study to control and manage the power grid. The results will promote economic development and sustainability of energy resources.Comment: 25 pages, 12 figures and 7 table

Short-term Volatility Estimation for High Frequency Trades using Gaussian processes (GPs)

The fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic. One of the complexities is the volatility associated with stock prices. Volatility is a tendency for prices to change unexpectedly [1]. Price volatility is often detrimental to the return economics, and thus, investors should factor it in whenever making investment decisions, choices, and temporal or permanent moves. It is, therefore, crucial to make necessary and regular short and long-term stock price volatility forecasts for the safety and economics of investors returns. These forecasts should be accurate and not misleading. Different models and methods, such as ARCH GARCH models, have been intuitively implemented to make such forecasts. However, such traditional means fail to capture the short-term volatility forecasts effectively. This paper, therefore, investigates and implements a combination of numeric and probabilistic models for short-term volatility and return forecasting for high-frequency trades. The essence is that one-day-ahead volatility forecasts were made with Gaussian Processes (GPs) applied to the outputs of a Numerical market prediction (NMP) model. Firstly, the stock price data from NMP was corrected by a GP. Since it is not easy to set price limits in a market due to its free nature and randomness, a Censored GP was used to model the relationship between the corrected stock prices and returns. Forecasting errors were evaluated using the implied and estimated data.Comment: 25 page

Estimating Short-Term Returns with Volatilities for High Frequency Stock Trades in Emerging Economies Using Gaussian Processes (GPs)

Fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic in nature. One of the complexities is the volatilities associated with stock prices. Price volatility is often detrimental to the return economics and thus investors should factor it in when making investment decisions, choices, and temporal or permanent moves. It is therefore crucial to make necessary and regular stock price volatility forecasts for the safety and economics of investors’ returns. These forecasts should be accurate and not misleading. Different traditional models and methods such as ARCH, GARCH have been intuitively implemented to make such forecasts, however they fail to effectively capture the short-term volatility forecasts. In this paper we investigate and implement a combination of numeric and probabilistic models towards short-term volatility and return forecasting for high frequency trades. The essence is that: one-day-ahead volatility forecasts were made with Gaussian Processes (GPs) applied to the outputs of a numerical market prediction (NMP) model. Firstly, the stock price data from NMP was corrected by a GP. Since it not easy to set price limits in a market due to its free nature, and randomness of the prices, a censored GP was used to model the relationship between the corrected stock prices and returns. To validate the proposed approach, forecasting errors were evaluated using the implied and estimated data

Independent and combined effects of improved water, sanitation, and hygiene, and improved complementary feeding, on child stunting and anaemia in rural Zimbabwe: a cluster-randomised trial.

BACKGROUND: Child stunting reduces survival and impairs neurodevelopment. We tested the independent and combined effects of improved water, sanitation, and hygiene (WASH), and improved infant and young child feeding (IYCF) on stunting and anaemia in in Zimbabwe. METHODS: We did a cluster-randomised, community-based, 2 × 2 factorial trial in two rural districts in Zimbabwe. Clusters were defined as the catchment area of between one and four village health workers employed by the Zimbabwe Ministry of Health and Child Care. Women were eligible for inclusion if they permanently lived in clusters and were confirmed pregnant. Clusters were randomly assigned (1:1:1:1) to standard of care (52 clusters), IYCF (20 g of a small-quantity lipid-based nutrient supplement per day from age 6 to 18 months plus complementary feeding counselling; 53 clusters), WASH (construction of a ventilated improved pit latrine, provision of two handwashing stations, liquid soap, chlorine, and play space plus hygiene counselling; 53 clusters), or IYCF plus WASH (53 clusters). A constrained randomisation technique was used to achieve balance across the groups for 14 variables related to geography, demography, water access, and community-level sanitation coverage. Masking of participants and fieldworkers was not possible. The primary outcomes were infant length-for-age Z score and haemoglobin concentrations at 18 months of age among children born to mothers who were HIV negative during pregnancy. These outcomes were analysed in the intention-to-treat population. We estimated the effects of the interventions by comparing the two IYCF groups with the two non-IYCF groups and the two WASH groups with the two non-WASH groups, except for outcomes that had an important statistical interaction between the interventions. This trial is registered with ClinicalTrials.gov, number NCT01824940. FINDINGS: Between Nov 22, 2012, and March 27, 2015, 5280 pregnant women were enrolled from 211 clusters. 3686 children born to HIV-negative mothers were assessed at age 18 months (884 in the standard of care group from 52 clusters, 893 in the IYCF group from 53 clusters, 918 in the WASH group from 53 clusters, and 991 in the IYCF plus WASH group from 51 clusters). In the IYCF intervention groups, the mean length-for-age Z score was 0·16 (95% CI 0·08-0·23) higher and the mean haemoglobin concentration was 2·03 g/L (1·28-2·79) higher than those in the non-IYCF intervention groups. The IYCF intervention reduced the number of stunted children from 620 (35%) of 1792 to 514 (27%) of 1879, and the number of children with anaemia from 245 (13·9%) of 1759 to 193 (10·5%) of 1845. The WASH intervention had no effect on either primary outcome. Neither intervention reduced the prevalence of diarrhoea at 12 or 18 months. No trial-related serious adverse events, and only three trial-related adverse events, were reported. INTERPRETATION: Household-level elementary WASH interventions implemented in rural areas in low-income countries are unlikely to reduce stunting or anaemia and might not reduce diarrhoea. Implementation of these WASH interventions in combination with IYCF interventions is unlikely to reduce stunting or anaemia more than implementation of IYCF alone. FUNDING: Bill & Melinda Gates Foundation, UK Department for International Development, Wellcome Trust, Swiss Development Cooperation, UNICEF, and US National Institutes of Health.The SHINE trial is funded by the Bill & Melinda Gates Foundation (OPP1021542 and OPP113707); UK Department for International Development; Wellcome Trust, UK (093768/Z/10/Z, 108065/Z/15/Z and 203905/Z/16/Z); Swiss Agency for Development and Cooperation; US National Institutes of Health (2R01HD060338-06); and UNICEF (PCA-2017-0002)

Solar power forecasting using Gaussian process regression

PhD (Statistics)Department of Mathematical and Computational SciencesSolar power forecasting has become an important aspect affecting crucial day-to-day activities in people's lives. Many African countries are now facing blackouts due to a shortage of energy. This has caused the urge to encourage people to use other energy sources to rise, resulting in different energy inputs into the main electricity grid. When the number of power sources being fed into the main grid increases, so does the need for efficient methods of forecasting these inputs. Thus, there is a need to come up with efficient prediction techniques inorder to facilitate proper grid management. The main goal of this thesis is to explore how Gaussian process predicting frameworks can be developed and used to predict global horiz0ontal irra- diance. Data on Global horizontal irrandiance and some weather variables collected from various meterological stations were made available through SAURAN (Southern African Universities Radiometric Network). The length of the dataset ranged from 496 to 17325 datapoints. Ve proposed using Gaussian process regression (GPR) to predict solar power generation. In South Africa, studies based on GPR regarding forecasting solar power are still very few, and more needs to be done in this area. At first, we explored covariance function selection, and a GPR was developed using Core vector regression (CVR). The predictions produced through this method were more accurate than the benchmark models used: Gradient Boosting Regression (GBR) and Support Vector Regression then, we explored interval estimation, Quantile re- gression and GPR were coupled in order to develop the modelling framework. This was also done to improve the accuracy of the GPR models. The results proved that the model performed better than the Bayesian Structural Time Series Regression. Ve also explored spatial dependence; spatio-temporal regression was incorporated into the modelling framework coupled with GPR. This was done to incorporate various weather stations' conditions into the modelling process. The spatial analysis results proved that GPR coupled with spatial analysis produced results that were superior to the Autoregressive Spatial analysis and benchmark model used: Linear Spatial analysis. The GPR results had accuracy measures that proved superior to the benchmark models. Various other tools were used to improve the accuracy of i the GPR results. This includes the use of combining forecasts and standardisation of predictions. The superior results indicate a vast benefit economic-wise because it allows those who manage the power grid to do so effectively and efficiently. Effective power grid management reduces power blackouts, thus benefitting the nation eco- nomically and socially.National Research Foundation (NRF

Twenty-Four-Hour Ahead Probabilistic Global Horizontal Irradiance Forecasting Using Gaussian Process Regression

Probabilistic solar power forecasting has been critical in Southern Africa because of major shortages of power due to climatic changes and other factors over the past decade. This paper discusses Gaussian process regression (GPR) coupled with core vector regression for short-term hourly global horizontal irradiance (GHI) forecasting. GPR is a powerful Bayesian non-parametric regression method that works well for small data sets and quantifies the uncertainty in the predictions. The choice of a kernel that characterises the covariance function is a crucial issue in Gaussian process regression. In this study, we adopt the minimum enclosing ball (MEB) technique. The MEB improves the forecasting power of GPR because the smaller the ball is, the shorter the training time, hence performance is robust. Forecasting of real-time data was done on two South African radiometric stations, Stellenbosch University (SUN) in a coastal area of the Western Cape Province, and the University of Venda (UNV) station in the Limpopo Province. Variables were selected using the least absolute shrinkage and selection operator via hierarchical interactions. The Bayesian approach using informative priors was used for parameter estimation. Based on the root mean square error, mean absolute error and percentage bias the results showed that the GPR model gives the most accurate predictions compared to those from gradient boosting and support vector regression models, making this study a useful tool for decision-makers and system operators in power utility companies. The main contribution of this paper is in the use of a GPR model coupled with the core vector methodology which is used in forecasting GHI using South African data. This is the first application of GPR coupled with core vector regression in which the minimum enclosing ball is applied on GHI data, to the best of our knowledge

Spatio-Temporal Forecasting of Global Horizontal Irradiance Using Bayesian Inference

Accurate global horizontal irradiance (GHI) forecasting promotes power grid stability. Most of the research on solar irradiance forecasting has been based on a single-site analysis. It is crucial to explore multisite modeling to capture variations in weather conditions between various sites, thereby producing a more robust model. In this research, we propose the use of spatial regression coupled with Gaussian Process Regression (GP Spatial) and the GP Autoregressive Spatial model (GP-AR Spatial) for the prediction of GHI using data from seven radiometric stations from South Africa and one from Namibia. The results of the proposed methods were compared with a benchmark model, the Linear Spatial Temporal Regression (LSTR) model. Five validation sets each comprised of three stations were chosen. For each validation set, the remaining five stations were used for training. Based on root mean square error, the GP model gave the most accurate forecasts across the validation sets. These results were confirmed by the statistical significance tests using the Giacommini–White test. In terms of coverage probability, there was a 100% coverage on three validation sets and the other two had 97% and 99%. The GP model dominated the other two models. One of the study’s contributions is using standardized forecasts and including a nonlinear trend covariate, which improved the accuracy of the forecasts. The forecasts were combined using a monotone composite quantile regression neural network and a quantile generalized additive model. This modeling framework could be useful to power utility companies in making informed decisions when planning power grid management, including large-scale solar power integration onto the power grid

Application of Jump Diffusion Models in Insurance Claim Estimation

We investigated if general insurance claims are normal or rare events through systematic, discontinuous or sporadic jumps of the Brownian motion approach and Poisson processes. Using firm quarterly data from March 2010 to December 2018, we hypothesized that claims with high positive (negative) slopes are more likely to have large positive (negative) jumps in the future. As such, we expected salient properties of volatile jumps on the written products/contracts. We found that insurance claims for general insurance quoted products cease to be normal. There exist at times some jumps, especially during holidays and weekends. Such jumps are not healthy to the capital structures of firms, as such they need attention. However, it should be noted that gaps or jumps (unless of specific forms) cannot be hedged by employing internal dynamic adjustments. This means that, jump risk is non-diversifiable and such jumps should be given more attention

Assessing effect of behaviour change on HIV/AIDS prevalence using a staged progression model

A staged progression model was proposed that is an intervention model incorporating behaviour change. Analysis of the intervention model revealed that the disease free equilibrium point is locally stable when the bifurcation parameter β < β * near R0 = 1. The endemic equilibrium point was shown to be locally stable using the centre manifold theorem and a Lyapunov function was used to show that the endemic equilibrium point is globally asymptotically stable. Results suggest that positive behaviour change is effective in reducing the HIV/AIDS prevalence for the first few years suggesting that positive behaviour change alone cannot be used effectively to control or eradicate HIV/AIDS. In the case of negative behaviour it was seen that negative behaviour change negatively impacts the population greatly during the first few years of the onset of the disease. However changes in patterns of HIV prevalence in Zimbabwe and most developing countries are quite recent and caution is required on the representativeness of the estimates and to note whether the observed changes are consistent with behaviour change and not the natural course of the HIV epidemic