ABSTRACT
This chapter addresses the problem of estimation for multi-step ahead portfolio predictors in the case when the asset return process is a vector-valued non-Gaussian process. It discusses discriminant analysis for quantile regression models. The chapter introduces a classification statistic for some categories, and propose the classification rule. It describes the problem of portfolio estimation under causal variables, and its application to the Japanese pension investment portfolio, whose main stream is mainly based on Kobayashi et al. In the estimation of portfolios, it is natural to assume that the utility function depends on exogenous variables. The chapter outlines estimation under the setting, where the optimal portfolio function depends on moments of the return process, and cumulants between the return process and exogenous variables.
