Temporal autocorrelation, spatial coherency, and their effects on voxel-wise parametric statistics were examined in BOLD fMRI null-hypothesis, or "noise," datasets. Seventeen normal, young subjects were scanned using BOLD fMRI while not performing any time-locked experimental behavior. Temporal autocorrelation in these datasets was described well by a 1/frequency relationship. Voxel-wise statistical analysis of these noise datasets which assumed independence (i.e., ignored temporal autocorrelation) rejected the null hypothesis at a higher rate than specified by the nominal alpha. Temporal smoothing in conjunction with the use of a modified general linear model (Worsley and Friston, 1995, NeuroImage 2: 173-182) brought the false-positive rate closer to the nominal alpha. It was also found that the noise fMRI datasets contain spatially coherent time signals. This observed spatial coherence could not be fully explained by a continuously differentiable spatial autocovariance function and was much greater for lower temporal frequencies. Its presence made voxel-wise test statistics in a given noise dataset dependent, and thus shifted their distributions to the right or left of 0. Inclusion of a "global signal" covariate in the general linear model reduced this dependence and consequently stabilized (i.e., reduced the variance of) dataset false-positive rates.