The low-pass filter used here is a Gaussian filter matched to a commonly
assumed HRF with parameters
and
(Friston et al. (1995)).
The histogram for low-pass
filtering demonstrates the idea of colouring, in that the whole
histogram is focused to a peak centered on a
close to
that entirely due to the low-pass filtering.
However, the standard deviation around this peak (standard deviation=17.6) is
greater than the standard deviation of the estimator of
(determined empirically on artificial data as standard deviation=12.9).
Since the data is showing a greater variability in
than there is in just estimating
,
this suggests the requirement for local estimation of autocorrelation
even when low pass filtering (colouring) is performed.
Although the autocorrelation estimate is made more robust, the
autocorrelation imposed by the colouring does not completely smother
the intrinsic autocorrelation.