Calculation of Solar Irradiation Prediction Intervals combining Volatility and Kernel Density Estimates

Significance Statement

The need for precise information on solar energy forecasting is of high importance to the energy demanding world as the reduced forecasting errors favor economic feasibility. Most of the previous techniques used in estimating solar energy forecasting solely depend on point forecasts. However, it was being discovered that both uncertainty and variability forecasting also play a major role in providing a long-time solar energy forecasting which would be of relevance for energy control.

Professor Juan R. Trapero from the University of Castilla-La Mancha in Spain discussed ways at which solar energy forecasting could be improved. The technique he used incorporates that of an uncertainty forecast, associated with the previous single use of point forecasts to derive prediction intervals. The research work is now published in peer-reviewed journal, Energy.

The prediction interval involves the combination of a non-parametric approach, which is the kernel density estimation and the second, a parametric approach which involves the volatility forecast model with adaptation of a time-varying variance solution followed by generalized autoregressive conditional heteroskedastic GARCH model and single exponential smoothing SES model estimations.

In the case study, global horizontal irradiance GHI data were provided by solar irradiance measurements for the Spanish Institute for Concentration Photovoltaics Systems. The author also employed a seasonal autoregressive integrated moving average ARIMA model, which was estimated with that of GARCH model.

From the results observed, the SES model provided a better volatility forecast compared to the GARCH model. Further results revealed that despite a higher hit rate observed for the non-parametric kernel density estimation, a higher average interval width was observed as unconditional coverage test was not passed. The latter result negates a desired prediction interval forecasting.

The parametric models of the GARCH and SES, however, passed the independence test unlike the non-parametric kernel density estimation, but a low hit rate and failure to unconditional coverage test was discovered when considering the Christoffersen conditional coverage test p-value.

The combination of non-parametric kernel density estimation approach and a parametric model of the SES showed a close hit rate value to the desired coverage which did not implicate a higher interval width. All the Christoffersen tests passed successfully, making the combined approach the best method in achieving the desired confidence level with a lower average interval width.

This study with the aid of the combined parametric and non-parametric approach provides a reliable prediction interval for solar energy forecasting.

Calculation of Solar Irradiation Prediction Intervals combining Volatility and Kernel Density Estimates - renewable energy global innovations

About the author

Juan R. Trapero is with the department of Business Administration at Universidad de Castilla-La Mancha (UCLM). He received the Ingeniero Industrial, M.B.A., and Ph.D. degrees from UCLM, Spain, in 2003, 2004, and 2008, respectively.

His research interests include system identification, forecasting and control, particularly applied to supply chain management and energy systems. He is one of the directors of the predictive analytics laboratory research group at UCLM.


Trapero, J.R. Calculation of Solar Irradiation Prediction Intervals combining Volatility and Kernel Density Estimates, Energy 114 (2016) 266-274.

University of Castilla-La Mancha, Department of Business Administration, Ciudad Real 13071, Spain.

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