A likelihood ratio and Markov chain‐based method to evaluate density forecasting

In this paper, we propose a likelihood ratio based method to evaluate density forecasts which can jointly evaluate the unconditional forecasted distribution and dependence of the outcomes. Unlike the well‐known Berkowitz test, the proposed method does not requires a parametric specification of time dynamics. We compare our method with the method proposed by several other tests and show that our methodology has very high power against both dependence and incorrect forecasting distributions. Moreover, the loss of power, caused by the non‐parametric nature of the specification of the dynamics, is shown to be small compared to Berkowitz test, even when the parametric form of dynamics is correctly specified in the latter method.