We now apply the procedure outlined in Section 2 to these lightcurves. To begin with, we must estimate the structure function for these data. Figure 2a shows a pair-wise estimate of the continuum band structure function obtained following the method of PRH92. This figure also shows our analytic approximation which is given by eqns (13) and (14) with
Using this covariance model, the PRH92 reconstruction was applied to the continuum light curve using N=5000 data points. A portion of the resulting reconstructed light curve is shown in Fig. 2b.
The next stage in the procedure is to convolve the reconstructed
continuum band light curve with a trial transfer function and compare
the result with the line band light curve in a 
sense. We can
then minimize the statistic in order to constrain free
parameters in the trial transfer function. We also minimize
over multiplicative and additive offsets between the continuum and line
band light curves, i.e. we set
and minimize over B and K as well as the parameters describing the
trial transfer function 
.
In this work, we choose two trial transfer functions. The first
represents the case where some fraction 
of the line band
flux is a delayed copy of the continuum band with a time delay 
:
The second represents the case where some fraction of the line
band flux is a delayed and smeared copy of the continuum band flux, where a
Gaussian kernel is used:
No extrapolations were performed during this procedure. In order to
avoid extrapolating, the statistic was calculated using a
subset of data points. For the trial transfer function 
, only
data during times 
were used to compute , where 
and
are the times of the start and end of the reconstructed
continuum light curve. For 
, is computed based upon
data from times 
.
Figure 3 shows the surfaces and confidence contours once this
procedure has been performed. When displaying the surfaces, we
plot 
in order to highlight the
topography of the surface near the global minimum in the surface. It
can be seen that the minimum of the 
2 surface corresponds to the
two lines 
and 
, i.e. no time delayed
component of the line band light curve is detected. Here we only show
the results for -- the results are trivial
(i.e. surface is completely flat) since the preferred solution
always have . The best fit values of the multiplicative
and additive constants are B=0.78 and K=0.90.
Figure 3: Results for MCG-6-30-15: surfaces and confidence
contours resulting from applying trial transfer function to the
reconstructed continuum light curves and comparing with the line band
light curve. Surfaces are plotted using as the ordinate in order to display the topography of the
region near the minimum. Contours are shown the following levels:
. The first three of
these contours correspond to 
, 90% and 95% for two
interesting parameters and are shown in bold.