SEMAINE D'ÉTUDE SUR LE ROLE DE L ANALYSE ECONOMETRIOUE ETC. 
155 
us consider a situation often encountered in applied work, na- 
mely, when the forecasts y,.,, ..., y,,, from model M are 
formed by means of ancillary forecasts of one or more exogen- 
ous variables (?); let y;,, ...,y;, be the quasi-forecasts 
obtained when the exogenous variables are known at the end 
of the forecast period and substituted for the ancillarv forecasts 
in M: then 
(76) 
is a measure of the accuracy of the forecast model M when 
those forecasting errors are removed which arise from im- 
perfect ancillary forecasting. 
Since the numerator and denominator of the JANUS quotient 
measure the deviations between theoretical and observed values 
in the observation range and the forecasting range, respectively, 
the JANUS quotient may be regarded as a criterion of stable 
model structure in the two ranges. To elaborate this point we 
shall consider two types of forecast 
(1) Forecastin 
i 
extrapolation (* 
This approach includes forecasting by deterministic extra 
polation, 
(77 a) vy,=f()+v. with E(y.\=f(# 
where f(¢) is a specified function, usually with parameters 
estimated from the ohservation range For example. f(#) max 
(3) Cf. HazLEwoop-VANDOME (1961), where forecasts of type y*,., are 
referred to as being obtained by extrapolation. For applications of the same 
device in unirelation models, see R. BENTZEL (1959). 
(*) See Ref. 43 for a more elaborate treatment. including application. 
M (75)-(76)\ th unirelation models 
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