PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - . 
there is a notable disparity, for in meteorology the emphasis 
on forecasting is the same in both approaches, whereas in 
econometrics this emphasis is more pronounced in short range 
than in long range forecasting. As is well known, econometric 
models of economic growth often are a hybrid between strict 
forecasting and economic programming and policy making. 
3.2. The Janus quotient: A predictive test criterion. 
The Janus quotient, an adaptation of the FISHERIAN F-ratio, 
has recently been proposed for purposes of predictive test- 
ing (7). Its formula is 
(75) 
LHI ; 
_ (n—ey 
ns 
: (a, — 7)? 
or | = + VJ? 
depending on whether we prefer to compare variances or stan- 
dard deviations. The test refers to a specified model, say M. 
The notations are a,, a,, ... for the actual observations, and 
Yi» V2» for the corresponding theoretical values as obtained 
from the model. Conceptually, the JANUS quotient refers to 
the instant between the past and the future, and as indicated 
by its metaphoric name, the JANUS quotient looks in two 
directions, backward in time over the observation range 
/=I, ..., n to form the denominator, forward in time over the 
prediction range t=#n+1, ..., #+m to form the numerator. 
The design of the JANUS quotient can be generalized and 
varied so as to adapt to different types of application. Let 
(3) See Ref. 43, also for further details. Cf. the U-criterion earlier pro- 
posed by H. Tue, Ref. 33, from which the J-criterion differs in being 
invariant to linear scale transformations. 
2] Wold - pag. 40