Solar irradiation prediction intervals based on Box-Cox transformation and univariate representation of periodic autoregressive model

Among the solutions to improve the integration of intermittent solar system, solar irradiation prediction is an essential process. This kind of prediction is a highly complex problem and requires highly robust and reliable statistical models for its simulation. The current research is devoted on the implementation of time series formalism which is based on the periodic autoregressive model (PAR) coupled with a power transform (Box-Cox; BC) of data to stabilize variance. A new and robust functional model is proposed based on the prediction intervals approach whose results in term of efficiency (prediction interval coverage probability) and interest (normalized mean interval length) are similar or better than classical prediction tools based on bootstrap utilization. In the deterministic case, the PAR coupled with BC transform gives more mixed results, but for most cases, the classical tools, like persistence, smart persistence, auto-regression, and artificial neural network fail to compete with PAR or PAR-BC models.