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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