The traditional approaches that employ the correlations between solar radiation and other measured meteorological variables are commonly utilized in studies. It is important to investigate the time-varying relationships between meteorological variables and solar radiation to determine which variables have the strongest correlations with solar radiation. In this study, the nonlinear autoregressive moving average with exogenous variable-generalized autoregressive conditional heteroscedasticity (ARMAX-GARCH) and multivariate GARCH (MGARCH) time-series approaches were applied to investigate the associations between solar radiation and several meteorological variables. For these investigations, the long-term daily global solar radiation series measured at three stations from January 1, 2004 until December 31, 2007 were used in this study. Stronger relationships were observed to exist between global solar radiation and sunshine duration than between solar radiation and temperature difference. The results show that 82-88% of the temporal variations of the global solar radiation were captured by the sunshine-duration-based ARMAX-GARCH models and 55-68% of daily variations were captured by the temperature-difference-based ARMAX-GARCH models. The advantages of the ARMAX-GARCH models were also confirmed by comparison of Auto-Regressive and Moving Average (ARMA) and neutral network (ANN) models in the estimation of daily global solar radiation. The strong heteroscedastic persistency of the global solar radiation series was revealed by the AutoRegressive Conditional Heteroscedasticity (ARCH) and Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) parameters. In order to illustrate the novelty and usefulness of the MGARCH model in energy applications, the conditional covariances and correlation coefficients between the global solar radiation and the meteorological variables among stations were obtained by dynamic conditional correlation (DCC) models. The resulting conditional covariances and correlation coefficients were found to be large. It was also observed that the conditional correlation coefficients between global solar radiation and sunshine duration were higher than that between global solar radiation and temperature difference. The results of this study will provide a better understanding of the associations between global solar radiation and meteorological variables and will provide a basis for the investigation of this relationship in models. (C) 2015 Elsevier Ltd. All rights reserved.