The evolution of the parameters may be referenced to previous parameter
values and the new observations by the measurement update
BT+l = 6T + KT+1 (YT+ xT+l T) (10)
where K represents the filter and is determined according to
i2 -
KT+l :T+ /TXT+lI T+l T+1/TxT+I + 2 (11)
The matrix E denotes the parameter covariance matrix. It is given
sequentially by
T+1I/,T T + Q (12)
with measurement update
ET+1 = T+l/T KT+l XT+l ET+l/T (13)
For interpretation of the expressions(9)-(13) the interested reader is
directed to Chow, Duncan and Horn, or Anderson and Moore. Implementation
of the updating recursions in (9)-(13) is straightforward given the
model developed in expressions (l)-(7). As stressed by Athans, the
Kalman filter algorithm should not be confused with the underlying
econometric model -- rather it should be viewed only as a means for
refining a model.
The value of the Kalman filter model stems from the systematic
manner in which new data may be incorporated. Expression (10) shows
that as the forecast error increases, greater weight is given to the
new observation in the determination of the updated parameters. However,