## 4 Discussion  
The present study was motivated by previous research by other authors such as [PERSON] (2017), [PERSON] et al. (2017), [PERSON] et al. (2018) and [PERSON] et al. (2019)) [PERSON] (2019), [PERSON] (2019), [PERSON] and [PERSON] (2019), among others, and the proposed method was developed. A new approach to solar power forecasting was done and the Gaussian process regression approach was used based on core vector regression. It produced better forecasts as a result of the best kernel which was selected.  
The results produced from this study were from the application of GPR coupled with core vector regression to produce real-time results. Lasso was performed on the data incorporating interactions to select variables for both UNV and SUN data. The application of the GPR involved the computation of a kernel, which was done by choosing an appropriate kernel from the four which were used. To improve forecasting results the MEB was adopted to come up with an appropriate kernel that would yield the best results. To achieve this, different kernels were used, that is: radial basis function, Matern, rational quadratic and dot product. Empirical results showed the radial basis function to be the best kernel since it had the smallest radius in all cases considered.  
GPR models were developed using the radial basis kernel. A comparison of GHI forecasts results of benchmark models SVM and GBM with the GPR was done and the GPR had the lowest mean absolute error and root mean square error for both radiometric stations. The mean absolute error for GPR on UNV data with interactions recorded the minimum values. The results showed that for both stations the radial basis kernel outperformed the other kernels producing the minimum enclosed ball. The decision was arrived at based on the radius of each kernel.  
Real-time analysis was done and dominant cycles were identified and the results show that for every hour the period was 15, this means that it took 15 min to come up with a cycle. The incorporation of real-time analysis enabled the analysis to reflect the cycle of  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **RMSE** & **MAE** & **Pbias** \\ \hline M1 & 34.1 & 20.9 & 0.2 \\ M2 & 148.4 & 102.8 & 1.3 \\ M3 & 2.7 & 2.1 & 0.2 \\ M4 & 122.5 & 64.9 & 43.4 \\ M5 & 168.5 & 126.6 & 7.1 \\ M6 & 142.7 & 103.8 & 0.6 \\ M7 & 173.9 & 116.9 & 11.9 \\ M8 & 164.7 & 110.5 & 10.6 \\ M15 over 1 h, so the analysis was done over 10 h showing a cycle of 150. This improved forecasting accuracy in the sense that analysis was done over a small interval of 10 h. It was observed when data were analysed that including interaction effects did not improve the results thus we discarded the inclusion of interaction effects.  
The modelling framework proposed in this study is important to system operators and decision-makers in power utility companies who require accurate forecasts of intermittent solar power which has to be integrated on the grid in balancing demand and supply of electricity in an effective way which is environmentally secure and also favours future economic prosperity of a country. The GPR models developed in this study are robust and as such can easily be adapted to forecasting different datasets such as wind speed, electricity demand, among others. The developed models can be used by system operators in short-term solar power forecasting.  
A limitation of the Gaussian process method is that despite its ability to compute the covariance functions, there is a lack of information on the uncertainty of the forecasts. The mean function is computed in this case using Bayesian regression but is not easily interpreted for Gaussian process models.