Volatility component models have received considerable attention recently, not only because of their ability to capture complex dynamics via a parsimonious parameter structure, but also because it is believed that they can handle well structural breaks or nonstationarities in asset price volatility. This paper revisits component volatility models from a statistical perspective and attempts to explore the stationarity of the underlying processes. There is a clear need for such an analysis, since any discussion about nonstationarity presumes we know when component models are stationary. As it turns out, this is not the case and the purpose of the paper is to rectify this. We also look into the sampling behavior of the maximum likelihood estimates of recently proposed volatility component models and establish their consistency and asymptotic normality.