Semi- and Nonparametric Forecasting

The time series methods we have discussed so far can be loosely classified as parametric (see, e.g., Chapter 5), and semi- and nonparametric (see, e.g., Chapter 7). For the parametric methods, usually a quite flexible but well-structured family of finitedimensional models are considered (Chapter 2), and the modeling process typically consists of three iterative steps: identification, estimation, and diagnostic checking. Often these steps are complemented with an additional task: out-of-sample forecasting. Within this setting, specification of the functional form of a parametric time series model generally arrives from theory or from previous analysis of the underlying DGP; in both cases a great deal of knowledge must be incorporated in the modeling process. Semi- and nonparametric methods, on the other hand, are infinite-dimensional. These methods assume very little a priori information and instead base statistical inference mainly on data. Moreover, they require “weak” (qualitative) assumptions, such as smoothness of the functional form, rather than quantitative assumptions on the global form of the model.