Stochastic modelling of global solar radiation measured in the state of Kuwait

Two stochastic models that capture the main features of daily exposure of global radiation in Kuwait are proposed. The development of these models is based on removing the annual periodicity and seasonal variation of solar radiation. Thus the daily radiation is decomposed as the sum of the trend component and a stochastic component. In many situations, there are dramatic changes in the radiation series through the year due to the condition of the weather, as is the case of the data from Kuwait. This would affect the accuracy of the model, and therefore the series is divided into two regimes: one corresponds to clear days where the value of the global radiation would be normal and the other to non-clear days where the value of global radiation would be very low. Then the trend component is expressed as a Fourier series taking into account such apparent breaks in the series. The stochastic component is first tested for linearity and Gaussianity and it is found that it does not satisfy these assumptions. Therefore, a linear time series model (ARMA modeling) may not be adequate and, to overcome this problem, a bilinear time series is used to model the stochastic component of daily global radiation in Kuwait. The method proposed considers first fitting an AR model to the data and then seeing whether a further reduction in the mean sum of squares can be achieved by introducing extra bilinear terms. The Akaike Information Criterion (AIC) is used to select the best model. Copyright (C) 2002 John Wiley Sons, Ltd.