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rows of ¢ and ¥, respectively. (The unqualified term « disturb- 
ance » will be reserved for the elements of u,.) 
All elements of e, v, and w, are composites of unobserv- 
ables; 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-regres- 
sive scheme (*!). Thus: 
5.13) 
(5.14) 
(5.15) 
where A,, A,, and A, are diagonal matrices of appropriate di- 
mension 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-cova- 
riance 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