A spatiotemporal auto-regressive moving average model for solar radiation

To investigate the variability in energy output from a network of photo-voltaic cells, solar radiation was recorded at ten sites every ten minutes in the Pentland Hills to the south of Edinburgh. We identify spatio-temporal auto-regressive moving average (STARMA) models as the most appropriate to address this problem. Although previously considered computationally prohibitive to work with, we show that by approximating using toroidal space and fitting by matching autocorrelations, calculations can be substantially reduced. We find a STAR(1) process with a first-order neighbourhood structure and a Matern noise process to provide an adequate fit to the data, and demonstrate its use in simulating realisations of energy output.