Model Specification and Design

Abstract

The mean response function μ _t+k of any given model defines, as a function of the step ahead index k, the implied form of the time series and is thus of fundamental interest in model design. The expectation of this, the forecast function f _t (k), provides the forecaster’s view of the expected development of the series and we focus on this, rather than the mean response itself, as the central guide to constructing appropriate models. This is purely convention on our part; equivalent discussion could be based on the mean response function instead. We begin with discussion of forecast functions derived from the various TSDLMs of the previous chapter. Together with complementary forms from models for the effects of independent variables, these provide essentially all practically important dynamic linear models.