The carbon market, as a market operating with carbon emission rights for core trading, plays an important role in reducing the production of greenhouse gases and controlling the risk of climate change caused by environmental pollution but also shows complex and changeable dynamic...

In this paper, we propose a likelihood ratio and Markov chain based method to evaluate density forecasting. This method can jointly evaluate the unconditional forecasted distribution and dependence of the outcomes. This method is an extension of the widely applied evaluation method for interval...