In functional magnetic resonance imaging statistical analysis there are problems with accounting for temporal autocorrelations when assessing change within voxels. Techniques to date have utilized temporal filtering strategies to either shape these autocorrelations or remove them. Shaping, or "coloring," attempts to negate the effects of not accurately knowing the intrinsic autocorrelations by imposing known autocorrelation via temporal filtering. Removing the autocorrelation, or "prewhitening," gives the best linear unbiased estimator, assuming that the autocorrelation is accurately known. For single-event designs, the efficiency of the estimator is considerably higher for prewhitening compared with coloring. However, it has been suggested that sufficiently accurate estimates of the autocorrelation are currently not available to give prewhitening acceptable bias. To overcome this, we consider different ways to estimate the autocorrelation for use in prewhitening. After high-pass filtering is performed, a Tukey taper (set to smooth the spectral density more than would normally be used in spectral density estimation) performs best. Importantly, estimation is further improved by using nonlinear spatial filtering to smooth the estimated autocorrelation, but only within tissue type. Using this approach when prewhitening reduced bias to close to zero at probability levels as low as 1 x 10(-5). Copyright 2001 Academic Press.