When performing statistical analysis of single-subject fMRI data, serial correlations need to be taken into account to allow for valid inference. Otherwise, the variability in the parameter estimates might be under-estimated resulting in increased false-positive rates. Serial correlations in fMRI data are commonly characterized in terms of a first-order autoregressive (AR) process and then removed via pre-whitening. The required noise model for the pre-whitening depends on a number of parameters, particularly the repetition time (TR). Here we investigate how the sub-second temporal resolution provided by simultaneous multislice (SMS) imaging changes the noise structure in fMRI time series. We fit a higher-order AR model and then estimate the optimal AR model order for a sequence with a TR of less than 600 ms providing whole brain coverage. We show that physiological noise modelling successfully reduces the required AR model order, but remaining serial correlations necessitate an advanced noise model. We conclude that commonly used noise models, such as the AR(1) model, are inadequate for modelling serial correlations in fMRI using sub-second TRs. Rather, physiological noise modelling in combination with advanced pre-whitening schemes enable valid inference in single-subject analysis using fast fMRI sequences.