Despite advances in modelling dynamic autoregulation, only part of the variability of cerebral blood flow velocity (CBFV) in the low frequency range has been explained. We investigate whether a multivariate representation can be used for this purpose. Pseudorandom sequences were used to inflate thigh cuffs and to administer 5% CO2. Multiple and partial coherence were estimated, using arterial blood pressure (ABP), end-tidal CO2 (EtCO2) and resistance area product as input and CBFV as output variables. The inclusion of second and third input variables increased the amount of CBFV variability that can be accounted for (p < 10−4 in both cases). Partial coherence estimates in the low frequency range (<0.07 Hz) were not influenced by the use of thigh cuffs, but CO2 administration had a statistically significant effect (p < 10−4 in all cases). We conclude that the inclusion of additional inputs of a priori known physiological significance can help account for a greater amount of CBFV variability and may represent a viable alternative to more conventional non-linear modelling. The results of partial coherence analysis suggest that dynamic autoregulation and CO2 reactivity are likely to be the result of different physiological mechanisms.