Abstract:
This study discusses an application of partially linear additive quantile regression
models in predicting medium-term global solar irradiance using data
from Tellerie radiometric station in South Africa for the period August 2009
to April 2010. Variables are selected using a least absolute shrinkage and
selection operator (Lasso) via hierarchical interactions and the parameters
of the developed models are estimated using the Barrodale and Roberts's
algorithm. The best models are selected based on the Akaike information
criterion (AIC), Bayesian information criterion (BIC), adjusted R squared
(AdjR2) and generalised cross validation (GCV). The accuracy of the forecasts
is evaluated using mean absolute error (MAE) and root mean square
errors (RMSE). To improve the accuracy of forecasts, a convex forecast combination
algorithm where the average loss su ered by the models is based
on the pinball loss function is used. A second forecast combination method
which is quantile regression averaging (QRA) is also used. The best set
of forecasts is selected based on the prediction interval coverage probability
(PICP), prediction interval normalised average width (PINAW) and prediction
interval normalised average deviation (PINAD). The results show that
QRA is the best model since it produces robust prediction intervals than
other models. The percentage improvement is calculated and the results
demonstrate that QRA model over GAM with interactions yields a small
improvement whereas QRA over a convex forecast combination model yields
a higher percentage improvement. A major contribution of this dissertation
is the inclusion of a non-linear trend variable and the extension of forecast
combination models to include the QRA.
