Capturing Long-Range Dependence and Harmonic Phenomena in 24-Hour Solar Irradiance Forecasting: A Quantile Regression Robustification via Forecasts Combination Approach

Abstract

The global horizontal irradiance data recorded at the earth's horizontal surface is a mixture of deterministic (extra-terrestrially) and stochastic components due to the ever-changing atmospheric conditions. The Box-Jenkins short memory stochastic models and their hybrid versions have been used successfully to forecast solar irradiance data. However, these models lack robustness and faulter for distant horizon forecasting such as more than 2 hours in the hourly case. Using a quantile regression model as both a robust benchmark and robustification model, we remedy this drawback by using long memory models and their hybrid versions in 24 hour ahead irradiance forecasting at three sites in South Africa (RVD, UPR and SUN). Results show that the inherent long memory is anti-persistent in all models but one that shows persistence. The forecasts from these long memory-based models are generally within the prediction interval of the benchmark model forecasts for two sites. Based on the RMSE, rRMSE, MAE, rMAE and the pinball loss function at the central quantile level and two extreme quantile levels, forecasts obtained through robustification via forecasts combinations with the quantile regression yield the best performance. The predictive ability of the best model before forecasts combination against the quantile regression model combined (robustified) model based Diebold-Mariano test rejected the null hypothesis of the same accuracy. As a follow up to distinguish which has a superior predictive accuracy "murphy diagrams" were used. For the RVD and UPR sites, the model based on forecast combination has the best predictive accuracy while the quantile regression based benchmark model has the best accuracy for the SUN data.

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

“…To incorporate volatility forecasts, Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and Single Exponential Smoothing (SES) estimation were used. Ranganai and Sigauke [12] applied additive quantile regression to model global horizontal irradiance. They used long-range dependence models on three sites based in South Africa and found that all the models were anti-persistent.…”

“…This means we are not concerned with the errors as long as they are less than ε. Thus, the line function of y is given in Equation (12). f (x) =< w, x > +b = ∑ w j x j + b, (12) where w ∈ X, (y, b) ∈ R and < ., .…”

“…Thus, the line function of y is given in Equation (12). f (x) =< w, x > +b = ∑ w j x j + b, (12) where w ∈ X, (y, b) ∈ R and < ., . > is the dot product of X. SVR makes use of kernels and control of marginal space solutions.…”

Forecasting Hourly Global Horizontal Solar Irradiance in South Africa Using Machine Learning Models

“…The results of the study showed that the QRA forecast combination model was the best forecasting model compared with other individual models in the study. A more recent study on global horizontal irradiance using South African data is that of [23]. In this study, [23] used three methods, seasonal autoregressive fractionally integrated moving average (SARFIMA), harmonically Coupled SARIMA (HCSAFRIMA) and Regression model with SARFIMA error terms (SARFIMAX) to address the long-range dependence inherent in the solar irradiance data from three radiometric stations in South Africa.…”

“…A more recent study on global horizontal irradiance using South African data is that of [23]. In this study, [23] used three methods, seasonal autoregressive fractionally integrated moving average (SARFIMA), harmonically Coupled SARIMA (HCSAFRIMA) and Regression model with SARFIMA error terms (SARFIMAX) to address the long-range dependence inherent in the solar irradiance data from three radiometric stations in South Africa. An additive quantile regression model was used for benchmarking with the three developed models.…”