Functional magnetic resonance imaging (fMRI) signal changes can be separated from background noise by various processing algorithms, including the well-known deconvolution method. However, discriminating signal changes due to task-related brain activities from those due to task-related head motion or other artifacts correlated in time to the task has been little addressed. We examine whether three exploratory fractal scaling analyses correctly classify these possibilities by capturing temporal self-similarity; namely, fluctuation analysis, wavelet multi-resolution analysis, and detrended fluctuation analysis (DFA). We specifically evaluate whether these fractal analytic methods can be effective and reliable in discriminating activations from artifacts. DFA is indeed robust for such classification. Brain activation maps derived by DFA are similar, but not identical, to maps derived by deconvolution. Deconvolution explicitly utilizes task timing to extract the signals whereas DFA does not, so these methods reveal somewhat different information from the data. DFA is better than deconvolution for distinguishing fMRI activations from task-related artifacts, although a combination of these approaches is superior to either one taken alone. We also present a method for estimating noise levels in fMRI data, validated with numerical simulations suggesting that Birn's model is effective for simulating fMRI signals. Simulations further corroborate that DFA is excellent at discriminating signal changes due to task-related brain activities from those due to task-related artifacts, under a range of conditions.