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Independent component analysis (ICA) has been widely applied to the analysis of fMRI data. Accurate estimation of the number of independent components (ICs) in fMRI data is critical to reduce over/underfitting. Various methods based on information theoretic criteria (ITC) have been used to estimate the intrinsic dimension of fMRI data. An important assumption of ITC is that the noise is purely white. However, this assumption is often violated by the existence of temporally correlated noise in fMRI data. In this study, we introduced a filtering method into the order selection to remove the autocorrelation from the colored noise by using the whitening filter proposed by Prudon and Weisskoff. Results of the simulated data show that the filtering method has strong robustness to noise and significantly improves the accuracy of order selection from data with colored noise. Moreover, the multifiltering method proposed by us was applied to real fMRI data to improve the performance of ITC. Results of the real fMRI data show that the proposed method can alleviate the overestimation due to the autocorrelation of colored noise. We further compared the stability of IC estimates of real fMRI data at order estimated by minimum description length criterion based on the filtered and unfiltered data by using the software package ICASSO. Results show that ICA yields more stable IC estimates using the reduced order by filtering.