Estimating the global order of the fMRI noise model

One of the major issues in GLM-based fMRI analysis techniques is the presence of temporal autocorrelations in the residual signal after regression. A possible correction method is that of prewhitening, which fits an autoregressive (or other) model to the residual and uses the expected temporal autocorrelations of the model to transform the data and design matrix such that the residual becomes white noise. In this article, a method is introduced to estimate the global autoregressive model order of a data set, based on the residuals after regression. The proposed global standardized partial autocorrelation (SPAC) method tests whether the spatial profile of partial autocorrelations at a certain lag is random, and uses random field theory to account for the spatial correlations typical for fMRI data. It is tested both on synthetic and fMRI data, and is compared to two traditional techniques for model order estimation.