REML gives median AR(1) estimates from -0.0134 to 0.0302 in six ds000102 runs.

This analysis compares lag-one correlation in ordinary least squares residuals with maximum likelihood (ML) and restricted maximum likelihood (REML) estimates under an exact stationary Gaussian AR(1) model. It uses 64 selected voxels from each of six public ds000102 runs and a primary mean model with trial, drift, and motion terms. The six REML medians range from -0.013440 to 0.030169; five are positive, while all six residual-correlation medians are negative. In 2,000 synthetic series generated under the stated design and AR(1) assumptions, REML has smaller absolute mean bias and root mean square error than residual correlation and ML at all four tested input values. This is a narrow comparison in three selected participants. The measured input covariance is unknown. The model assumptions may be incorrect, and these results do not establish noise independence, biological causality, or correct task inference.

restricted maximum likelihood · REML · AR(1) · fMRI · residual covariance · noise estimation · synthetic simulation