Prewhitening requires a robust estimator of the autocorrelation to maintain low bias and Friston et al. (2000) suggests that current techniques for estimating the autocorrelation are not accurate enough to give prewhitening acceptable bias. However, in Friston et al. (2000) efforts were focussed on using global estimates of autocorrelation for reasons of computational efficiency. In this paper local estimation techniques were considered and were found to perform at acceptable speeds (less than 5 minutes for the null datasets used in this paper).
One interesting characteristic of the calibration/bias plots in
figures 13-16
is that the empirically obtained probabilities are predominantly less than
the expected theoretical probabilities. It is not clear why this should be
the case. One possibility is that
all of the autocorrelation techniques are overestimating the
noise at low frequency. This could be a symptom of the trade-off between being
sufficiently flexible to model the low frequency components and avoiding
over-fitting at higher frequencies.
One solution could be to use a nonparametric model
fitted in the spectral domain which allows more flexibility at low frequencies
(Marchini and Ripley, 2000). In this paper nonlinear spatial smoothing is used to
regularise spatially and this allows the use of a more flexible 
Tukey
window, whilst at the same time avoiding over-fitting.
This reduces bias to close to zero.
In similar work by Burock and Dale (2000) a first order Autoregressive model with an extra white noise component is used when performing prewhitening on randomised ISI designs. They also demonstrate the efficiency gained through prewhitening and show that their estimates are unbiased. However, they do not appear to examine the bias as far into the tail as in this paper. Perhaps more importantly, the plots used to examine the bias are on a linear scale and this makes assessment of bias at low probabilities very difficult to assess. In this paper we use a log-log scale and findings suggest that bias is evident in the tail for general order AR models.
It would also be interesting to know more about the source of temporal autocorrelation, particularly with regards to its spatial nature. In particular, it would be interesting to understand the source of the increased autocorrelation in the grey-matter, whether or not it is physiological in origin and how it varies within the grey-matter itself.