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where vt and ut are the white noise processes of filtered Y and X
series, respectively, at is the dynamic shock model error process, and
V(B) and Y(B) are polynomials of the lag operator B. Since by defini
tion ut and vt are orthogonal to themselves; e.g., COV(ut,u8) 0, for
every t*s, then each parameter coefficient in V(B) is simply the bivari
ate regression coefficient relating vt to u^^ given as
V, ^ rAA(k)
k a uv
ut
where crv and o are the standard error of the innovation series and k
t t
is the lag of the residual cross correlation.
Dynamic Regression Transfer Function
Given that the parameter coefficients of V(B) have been identified
and the order of the polynomial is known, the original filter expres
sions
9(B)Xt ut