In this paper, the dynamic relationship between global surface temperature (global warming) and global carbon dioxide emission (CO 2 ) is modelled and analyzed by causality and spectral analysis in the time domain and frequency domain, respectively. Historical data of global CO 2 emission and global surface temperature anomalies over 129 years from 1860-1988 are used in this study. The causal relationship between the two phenomena is first examined using the Sim and Granger causality test in the time domain after the data series are filtered by ARIMA models. The Granger causal relationship is further scrutinized and confirmed by cross-spectral and multichannel spectral analysis in the frequency domain. The evidence found from both analyses proves that there is a positive causal relationship between the two variables. The time domain analysis suggests that Granger causality exists between global surface temperature and global CO 2 emission. Further, CO 2 emission causes the change in temperature. The conclusions are further confirmed by the frequency domain analysis, which indicates that the increase in CO 2 emission causes climate warming because a high coherence exists between the two variables. Furthermore, it is proved that climate changes happen after an increase in CO 2 emission, which confirms that the increase in CO 2 emission does cause global warming.