ABSTRACT
The Weiner-Kolmogorov prediction formulas allow us to write the conditional
expectations in (3.11') in a simple fashion:
(3.13)
where [ ]+means "ignore negative powers of L." Substituting expression
(3.13) into (3.11') and rearranging, yields:
(3.14)
= !_ta (L) [ 1-L nJlw + l_~S (L) n L -1 t-1 n L
1-L -+
But, we can also use the Heinter-Kolrnogorov prediction formula to write the
E R = 1)-(L)] w + f<I(L)] v t-l n,t [ L J+ t-1 [ L ]+ t-1"
(3.15)
in (3.12) implied by the theory of the term structure of the forward premium:
G(L) [1-L=nJ] [ L 1-L 1 +
(3.16)
(§(L)] = .!_ f]l(L) (1-L=nJ] • [ L ]+ n L L l-L 1 +
moving averages and so we use an alternative representation of (R1 , R ). ,t n,t
(R1 t' R ), imposed by rational expectations. By our assumptions of , n,t
and vt are the same):
Rl,t = E aiRl,t-i + E ~iRn,t-i + wt i=l i=l
(3.17a)
Rn,t E y .Rl i + E 0iRn, t-i + vt i=l l. ,t-i=l
(3.17b)
where
{wt' vt} is the innovation in the (R1 , R ) process; the errors are con-,t n,t
can be rewritten as: 1
1Equation (3.18) amounts to rewriting an Mth order difference equation as a vector first order system.
