-11-
with the stochastic specification that
E(VT) = 0 (23a)
E(VTVT') = 4IT + AT(IT-1Q )AT = T (23b)
In (23b) Q is a block diagonal matrix whose i block consists of
the varying parameter covariance matrix of the ith equation. Unless
Qi = 0, note that Dii in equation (23b) will differ from the same
expression in (16b). Since nT is the sum of a diagonal and a block
diagonal matrix, this result preserves the recursiveness of the system.
Estimation of the parameters at time T now follows from appli-
cation of GLS to the system. Specifically
AT = (ZT1T ZT) ZT T Vec(YT) (24)
with the structural parameter covariance matrix for the ith equation
denoted by
Var(AiT) = (ZiT iTZiT)1 T (25)
Forecasts are generated from the reduced form implied by the varying
structure. Thus, the reduced form parameters not only carry information
concerning structural exclusion restrictions but also translate the
varying parameter process from the structure to the reduced form. In
general, the structural coefficients can be updated using the sequential
algorithms presented in expression (9)-(13) and forecasts would be made
using the updated restricted reduced form parameter matrix
11T+/T = T+ T+/T (26)