SEMAINE D’ETUDE SUR LE ROLE DE 1. ANALYSE ECONOMETRIOUE ETC. 
147 
parameters so that all relations in the primary form make 
eo 1pso predictors. 
The notation RFUE-system serves to emphasize that the 
reduced form but in general not the primary form makes a set 
of eo ipso predictors. In PFUE-svstems it is the other way 
around (19). 
(3) BEID- (bi-expectational interdependent) systems. 
Here, to repeat, both the primary and the reduced form are 
specified in terms of eo ipso predictors. 
Illustrations ('7). Whereas an ID-system and the cor- 
responding PFUE- and BEID-systems in general generate 
three different stochastic processes, the following three models 
have been designed so as to generate one and the same stoch- 
astic process. Hence if a realization has been generated from 
one of the models, the realization by itself cannot indicate from 
which one of the three models it has been generated. The 
process involves two endogenous variables p,, g, and no exogen- 
ous variable, and it is stationary and Gauss-MARKOVIAN with 
the following nine parameters, 
‘61) 
E, 
(62) 
- x 
4 
1° 
A 
(16) PFUE-systems are what I have earlier, Refs. 12, 28 and 30, called 
implicit or conditional causal chain (CCC-) svstems. covering as special cases 
circular and bicausal chain systems. 
(7) Models (65)-(67) and (68)-(70) are quoted from Ref. 30. I am indebted 
to Dr. LYTTKENS for pointing out an erratum in Ref. 30, p. 394, where 
the relation that corresponds to (69 ¢) is wrongly stated as E(v;, vi. =) =O. 
The erratum does not affect the statement that the three models there 
considered define one and the same stochastic process, but it does destroy 
the Markov character of model (68)-(70). For example in (66b) we have 
E(qlp.1) = Elg.lPr-1, Pi2G. 2 Dr as 
but in general not so in (7ob) 
Wold - pag. 33