The scientific and clinical importance of cerebral hemodynamics has generated considerable interest in their quantitative understanding via computational modeling. In particular, two aspects of cerebral hemodynamics, cerebral flow autoregulation (CFA) and CO2 vasomotor reactivity (CVR), have attracted much attention because they are implicated in many important clinical conditions and pathologies (orthostatic intolerance, syncope, hypertension, stroke, vascular dementia, mild cognitive impairment, Alzheimer's disease, and other neurodegenerative diseases with cerebrovascular components). Both CFA and CVR are dynamic physiological processes by which cerebral blood flow is regulated in response to fluctuations in cerebral perfusion pressure and blood CO2 tension. Several modeling studies to date have analyzed beat-to-beat hemodynamic data in order to advance our quantitative understanding of CFA-CVR dynamics. A confounding factor in these studies is the fact that the dynamics of the CFA-CVR processes appear to vary with time (i.e., changes in cerebrovascular characteristics) due to neural, endocrine, and metabolic effects. This paper seeks to address this issue by tracking the changes in linear time-invariant models obtained from short successive segments of data from ten healthy human subjects. The results suggest that systemic variations exist but have stationary statistics and, therefore, the use of time-invariant modeling yields "time-averaged models" of physiological and clinical utility.