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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