The environmental deterioration and resulting climate change have become one of the major challenges that human has faced in recent years. Carbon emission trading, as an effective economic tool to deal with climate change issues, has attracted widespread attention. As a major carbon emitter, China plays an important role in combating global climate change. Based on the carbon emission trading price data of China's Hubei Emission Exchange, a Vector Auto-Regressive (VAR)-Vector Error Correction (VEC) model is first used to investigate the dynamic relationship between energy price, macroeconomic indicators, air quality, and carbon emission trading price. The results show that there is a long-term equilibrium relationship between carbon emission trading price and these indicators. When the carbon emission price is too high and deviates from the long-term equilibrium value, it will slowly decline to reach the long-term equilibrium value. The price of carbon emission trading is largely affected by macroeconomic indicators among all these influencing factors. In addition, a Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH) model is used to explore the fluctuation characteristics of China's carbon emission trading price. It is found that the return series of carbon emission price are consistent with the characteristics of financial time series, such as fluctuation aggregates, spikes and thick tails, and non-normal distribution. There is a positive leverage effect for the fluctuation of China's carbon emission price. It is further found that external bad news has a greater impact on the fluctuation of China's carbon emission trading price than good news.