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the fore, inasmuch as VR-, CC- and ID-systems make use of
the chain principle in extracting inference from the model. If
a forecast is to span 18 months, say, and weekly data are
available, a model of type (6) with weekly data would require as
much as #8 links, a design that involves the danger that the
forecasting errors will aggravate by accumulation; it would
then be attractive to build a model of type (10) or (18) on the
basis of quarterly data, say, a model that exploits the inter-
relations between variables as observed during one and ‘the
same period; such an approch would require only 6 links in
the forecasting procedure. À specific point in this connection
is that in economic statistics the observational errors are in
practice relatively more important if the aggregation period is
short (°); hence there will be a downward tendency in the
magnitude of regression coefficients, and the accuracy of the
forecast will not be optimal if the aggregation period is too
short. To put it otherwise, if the disaggregation goes too far it
works against the law of large numbers, and thereby attenuates
the inference from the model. This is just one aspect of the
problem what period of aggregation is optimal in the design
of the model, a highly important, many-faceted and difficult
question that falls outside the scope of this brief review.
The chain principle is a unifving feature of VR- CC- and
[D-systems. More specifically, the forecasts are generated by
the chain principle as applied to the reduced form, and this
has the same mathematical structure in all three models, as
seen from (8)-(g), (15)-(17) and (21)-(23). At the same time
the chain principle brings in relief that the models work at
three different levels of generalization. Thus in VR-systems (8)
the primary form coincides with the reduced form; in CC-
systems the primary form (12) is transformed to the reduced
form (15) by a sequence of iterated substitutions: in ID-svstems
(°) Ref. 15, Appendix B, discusses this point with reference to correla-
tion coefficients, and the same argument applies to regression coefficients.
2] Wold - pag. 13
