SEMAINE D'ÉTUDE SUR LE ROLE DE L ANALYSE ECONOMETRIOUE ETC.

155

us consider a situation often encountered in applied work, namely,
 when the forecasts y,.,, ..., y,,, from model M are
formed by means of ancillary forecasts of one or more exogenous
 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 imperfect
 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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