A comparative study of the stochastic models and harmonically coupled stochastic models in the analysis and forecasting of solar radiation data

Abstract

Extra-terrestrially, there is no stochasticity in the solar irradiance, hence deterministic models are often used to model this data. At ground level, the Box-Jenkins Seasonal/Non-seasonal Autoregressive Integrated Moving Average (S/ARIMA) short memory stochastic models have been used to model such data with some degree of success. This success is attributable to its ability to capture the stochastic component of the irradiance series due to the effects of the ever-changing atmospheric conditions. However, irradiance data recorded at the earth’s surface is rarely entirely stochastic but a mixture of both deterministic and stochastic components. One plausible modelling procedure is to couple sinusoidal predictors at determined harmonic (Fourier) frequencies to capture the inherent periodicities (seasonalities) due to the diurnal cycle, with SARIMA models capturing the stochastic components. We construct such models which we term, harmonically coupled SARIMA (HCSARIMA) models and use them to empirically model the global horizontal irradiance (GHI) recorded at the earth’s surface. Comparison of the two classes of models shows that HCSARIMA models generally out-compete SARIMA models in the forecasting arena.