The Set of Admitted Models and the Way in Which the Selection is Carried Out
The problem of the selection of a forecasting model has presented itself in practice since long. As we have argued in the previous sections, the principles that are used in the selection are not at all uniform and often obscure. Many questions which are all in fact aspects of the same general selection problem are often answered differently. It is interesting to notice that some of the indicators used are in fact specific forms of the standard proposed here. This will be demonstrated in this chapter in Section 4.2. For this purpose first the criterion for selection is broken up in its component parts. The earlier restrictions remain valid especially the fact that the set is only composed of reduced forms of linear stochastic models with unknown coefficients and normally distributed disturbances with expectation 0 and an unknown but constant variance-covariance matrix. Section 4.3 deals with the meaning of these restrictions and with the question whether testing is necessary and, if so, which testing. In Section 4.4 the question arises to what extent efficiency in the selection can be achieved. As it is, one need not always construct the whole set of admitted models before selecting the optimal procedure. Sometimes it is already apparent during the testing that a model can indeed be admitted but does not have a chance of being chosen in the selection. One would better drop such a model at once. We shall call such a model non-relevant then. So, in fact, the selection takes place on the basis of the set of relevant admitted models. Finally, in the last section of this chapter a few problems are broached, connected with the use of lagged process variables.
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