In-sample density forecasting is defined as forecasting a structured density in regions where the density is not observed. After reviewing the recent density forecasting models, this paper attempts to generalize such density forecasting models and to develop some theory for this class of models. Here, the density in such regions where it is not observed is formulated by structural assumptions on the density that allows exact extrapolation. In this regard, the structural assumption is made such that the density is a product of one-dimensional functions. The structured in-sample density forecasting model is described and it is shown that the model can be estimated under weak conditions. The new approach proposed to the estimation of the model is then presented in detail . The proposed model is, in fact, developed under the assumption that the data are observed in continuous time and nonparametric smoothing methods are applied. The theoretical properties of the proposed method are discussed. The performance of the new approach is illustrated with both simulation and numerical examples and the results are discussed at length. (26 refs.)
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