It has recently become evident that the functional connectome of the human brain is a dynamical entity whose time evolution carries important information underpinning physiological brain function as well as its disease-related aberrations. While simple sliding window approaches have had some success in estimating dynamical brain connectivity in a functional MRI (fMRI) context, these methods suffer from limitations related to the arbitrary choice of window length and limited time resolution. Recently, Generalized autoregressive conditional heteroscedastic (GARCH) models have been employed to generate dynamical covariance models which can be applied to fMRI. Here, we employ a GARCH-based method (dynamic conditional correlation - DCC) to estimate dynamical brain connectivity in the Human Connectome Project (HCP) dataset and study how the dynamic functional connectivity behaviors related to personality as described by the five-factor model. Openness, a trait related to curiosity and creativity, is the only trait associated with significant differences in the amount of time-variability (but not in absolute median connectivity) of several inter-network functional connections in the human brain. The DCC method offers a novel window to extract dynamical information which can aid in elucidating the neurophysiological underpinning of phenomena to which conventional static brain connectivity estimates are insensitive.