SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 417

rows of ¢ and ¥, respectively. (The unqualified term « disturbance
 » will be reserved for the elements of u,.)
All elements of e, v, and w, are composites of unobservables;
 it is hardly restrictive to assume:
(A.1) Every element of e, v, or w, is uncorrelated in
probability with all present or past values of any other element
of any of these vectors. The vectors can always be redefined
to accomplish this.
We shall assume that each element of each of these implicit
disturbance vectors obeys a (different) first-order auto-regressive
 scheme (*!). Thus:

5.13)

(5.14)

(5.15)

where A,, A,, and A, are diagonal matrices of appropriate dimension
 and e,*, v,*, and w,* are vectors of non-auto-correlated
random variables. Assuming that the variance of each element
of e,, v,, and w, is constant through time, the diagonal elements
of A, A,, and A, are first-order auto-correlation coefficients
and are thus each less than one in absolute value.
Now let A,, A, and A, be the diagonal variance-covariance
 matrices of the elements of ¢,, v,, and w,, respectively.
In view of (A.1) and (5.13)-(5.15) it is easy to show that (5 =
implies:

(5.16)

V °

-

Yi -

-

!
o

+

(*") Auto-regressive relations of higher orders could be considered in
principle, but this would rather complicate the analysis. We shall thus
assume that first-order relationships are sufficiently good approximations.
If higher-order relationships are involved there is no essential change ir
the qualitative results

Fisher - pag. 33