Box–Jenkins multiplicative ARIMA modeling for prediction of solar radiation: a case study

Abstract

This study deals with stochastic modeling of solar radiation in all sky conditions and presents an effort to predict and analyze the future trends of monthly insolation based on time series analysis. Multiplicative seasonal autoregressive integrated moving average (ARIMA) model, using Box–Jenkins approach, has been utilized for simulating monthly average insolation data retrieved from NASA POWER (Prediction of Worldwide Energy Resource) data over the study area. The satellite dataset for a period of 34 years has been analyzed for modeling monthly average insolation. The insolation data time series examined by differencing and autocorrelation functions clearly indicates the existence of seasonality. Various multiplicative seasonal ARIMA models developed were validated by assessing various estimation parameters and their performance was evaluated by utilizing different selection measure criterion. The ARIMA (1, 0, 1) × (0, 1, 1)12, possessing minimum value of these criteria, was identified as the most adequate model. Forecasting of insolation was performed through selected models at 95% confidence interval. Results also reveal that ARIMA (1, 0, 1) × (0, 1, 2)12 produces minimum mean percentage error (MPE) in the forecast. As the difference in MPE for ARIMA (1, 0, 1) × (0, 1, 1)12 and ARIMA (1, 0, 1) × (0, 1, 2)12 is marginal (i.e., 0.004), the two models present minimal differences in estimated values and are therefore, reckoned as adequate for forecasting solar radiation.