In a subject-level GLM model (3dREMLfit), we tried to model the global effect caused by respiratory noise using global signal covariate(s) (e.g., WM and/or CSF mean). It significantly improved the contrast between two tasks involving different ventilation patterns. However, it's known that different regions in the brain may have different latencies and amplitudes for the global artifacts even though their temporal pattens may be quite close. The question is whether the autoregressive ARMA(1,1) modeling works on covariates and takes care of the latency-variation problem automatically or not. Do we need to temporally shift the global signal as multiple covariates to work around the problem?