Cerebral autoregulation is the process by which blood flow to the brain is maintained despite changes in arterial blood pressure (ABP) assuming other physiological condition changes to be small. The detection of cerebral autoregulation plays an increasingly important role in diagnosis, monitoring and prognosis of cerebrovascular disease clinically. ABP was measured using infrared plethysmography device (Finapres) and middle cerebral artery flow velocity (MCAv) data were obtained by two approaches: simulation and measurement. In the simulation approach, Ursino's multi-compartmental, nonlinear, physiological model was used to simulate MCAv with measured ABP as an input. The physiological model provides an ideal platform in order to analyse the relationship between the simple, linear model (ARX model) order choices, noise level and ABP variability while maintaining the constant state of cerebral autoregulation. In comparison, an ARX was validated in cerebral autoregulation assessment, fitted by the measured data. In this approach, MCAv and end-tidal pCO₂ were simultaneously measured using transcranial Doppler ultrasound and capnography, respectively. One baseline and two ABP manipulation experiments under both normocapnia and hypercapnia conditions were carried out. It has shown been that the setting of the ARX model orders in the range of 1 < na < 2 and 3 < nb < 5 is a reasonable trade-off between prediction accuracy of the model, parameter parsimony, and reliability of step response according to the simulation results. Step responses of ARX models trained by three kinds of datasets are not significantly different, suggesting that cerebral autoregulation may not be directly related to ABP-stimulating techniques. Moreover, the ARX model enables not only sinusoidal data but also spontaneous and step-like changes to be used to estimate the phase difference between ABP and MCAv.