Predictive Density Evaluation. Revised.

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 specification 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 (2005a,b,c,d), 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.