and Company. The exchange ratio is 0.37. The deal was announced Octo-
ber 19, 1998, and completed January 13, 1999. Notice that smaller lags tend
to follow the data more closely. Increasing the lag results in greater smooth-
ing and greater deviations from the data.
We also have a plot of the cost function as discussed for various lags. See
Figure 12.2.
Note that the minimum cost value occurs at lag 3. A visual examination
of the smoothed series for lag 3 against the series for other lags shows that
it is indeed a reasonable choice.
Thus, a low value for the lag parameter dimplies a noisy set of state es-
timates, making the Kalman filter very sensitive to the observations. Alter-
nately, a high value for the lag parameter ddenotes a smoother set of states
and the observations are largely ignored. The most suitable value for the lag
parameter is one that minimizes the cost function.
APPLICATIONS TO TRADING
Along with the smoothed version of the spread, at every time instant, the
Kalman filter also estimates the error standard deviation at each point. This
can be treated as error bands, about a mean estimate, similar to bollinger
Spread Inversion 197
FIGURE 12.2 Model Choice ( MCK-HBOC).024 6 88910111213Model Cost