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the varying parameter structural model uses its restricted reduced form

for prediction, but this reduced form is obtained by updating the

structure -- not by updating the reduced form directly as in the

second case.

 The results in Table 3 indicate that the varying parameter approach

achieves a respectable improvement in forecast accuracy over the constant

parameter model. However, the substantial increase in the forecast

errors from the one period ahead predictions to the two-period ahead

case suggests that the variances on the varying parameters are not allow-

ing sufficiently rapid adjustment of the parameters over the forecast

interval. ,This is evident by considering the results in Table 3. Recall

that for both forecast intervals the reduced form design matrix either

consists of variables lagged two periods or deterministic components.

Thus, the only difference between the one and two period ahead fore-

casts is the amount of information available with which to estimate the

coefficients. Apparently the varying parameters are not adjusting

rapidly enough to the new information conveyed by the measurement up-

dates with the result that two periods ahead forecast accuracy suffers

dramatically.

 SUMMARY AND CONCLUSIONS


 The varying parameter, generalized least squares, and Kalman filter

models may all be related algebraically. By imposing a varying parameter

structure on a behavioral relation, the corresponding filtering equation

may be derived so as to permit efficient updating. A properly specified