Predictive Density Evaluation

This Chapter discusses estimation, specification testing, and model selection of predictive density models. In particular, predictive density estimation is briefly discussed. And a variety of different specifications and model evaluation tests due to various authors including Christoffersen and Diebold (2000), Diebold Gunther and Tay (1998), Diebold Hahn and Tay (1999), White (2000), Bai (2003), Corradi and Swanson (2003 and 2004(a),(b),(c)), Hong and Li (2003), and others are reviewed. Extensions of some existing techniques to the case of out-of-sample evaluation are also provided, and asymptotic results associated with these extensions are outlined.