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Pre-whitening of fMRI time-series is commonly performed to address temporal autocorrelations. The pre-whitening procedure requires knowledge of the spatially dependent autocorrelations, which in turn must be estimated from the observed data. The accuracy of the autocorrelation estimation algorithm is important because biased autocorrelation estimates result in biased test statistics, thereby increasing the expected false-positive and/or false-negative rates. Thus, a methodology for testing the accuracy of autocorrelation estimates and for assessing the performance of today's state-of-the-art autocorrelation estimation algorithms is needed. To address these problems, we propose an evaluation framework that tests for significant autocorrelation bias in the model residuals of a general linear model analysis. We apply the proposed testing framework to 18 pre-surgical fMRI mapping datasets from ten patients and compare the performance of popular fMRI autocorrelation estimation algorithms. We also identify five consistent spectral patterns representative of the encountered autocorrelation structures and show that they are well described by a second-order/two-pole model. We subsequently show that a nonregularized, second-order autoregressive model, AR(2), is sufficient for capturing the range of temporal autocorrelations found in the considered fMRI datasets. Finally, we explore the bias versus predictability tradeoff associated with regularization of the autocorrelation coefficients. We find that the increased bias from regularization outweighs any gains in predictability. Based on the obtained results, we expect that a second-order, nonregularized AR algorithm will provide the best performance in terms of producing white residuals and achieving the best possible tradeoff between maximizing predictability and minimizing bias for most fMRI datasets.