Statistical analysis of multi-day solar irradiance using a threshold time series model

The analysis of solar irradiance has important applications in predicting solar energy production from solar power plants. Although the sun provides every day more energy than we need, the variability caused by environmental conditions affects electricity production. Recently, new statistical models have been proposed to provide stochastic simulations of high-resolution data to downscale and forecast solar irradiance measurements. Most of the existing models are linear and highly depend on normality assumptions. However, solar irradiance shows strong nonlinearity and is only measured during the day time. Thus, we propose a new multi-day threshold autoregressive model to quantify the variability of the daily irradiance time series. We establish the sufficient conditions for our model to be stationary, and we develop an inferential procedure to estimate the model parameters. When we apply our model to study the statistical properties of observed irradiance data in Guadeloupe island group, a French overseas region located in the Southern Caribbean Sea, we are able to characterize two states of the irradiance series. These states represent the clear-sky and non-clear sky regimes. Using our model, we are able to simulate irradiance series that behave similarly to the real data in mean and variability, and more accurate forecasts compared to linear models.