Simulation of radiation is one of the most important issues in solar utilization. Time series models are useful tools in the estimation and forecasting of solar radiation series and their changes. In this paper, the effectiveness of autoregressive moving average (ARMA) models with various generalized autoregressive conditional heteroskedasticity (GARCH) processes, namely ARMA-GARCH models are evaluated for their effectiveness in radiation series. Six different GARCH approaches, which contain three different ARMA-GARCH models and corresponded GARCH in mean (ARMA-GARCH-M) models, are applied in radiation data sets from two representative climate stations in China. Multiple evaluation metrics of modeling sufficiency are used for evaluating the performances of models. The results show that the ARMA-GARCH models are effective in radiation series estimation. Both in fitting and prediction of radiation series, the ARMA-GARCH(-M) models show better modeling sufficiency than traditional models, while ARMA-EGARCH-M models are robustness in two sites and the ARMA-sGARCH-M models appear very competitive. Comparisons of statistical diagnostics and model performance clearly show that the ARMA-GARCH-M models make the mean radiation equations become more sufficient. It is recommended the ARMA-GARCH(-M) models to be the preferred method to use in the modeling of solar radiation series. (C) 2015 Elsevier Ltd. All rights reserved.