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Statistical Inference for Volatility Component Models

The volatility component models have received much 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 non-stationarities in asset price volatility. The paper studies the distributional properties of various volatility component models. Sufficient conditions for the existence or/and uniqueness of (strictly) stationary (ergodic) solutions with mixing property to the volatility component models are derived. Hence, the paper revisits the component models from a statistical perspective and attempts to explore the stationarity and mixing properties of the underlying processes. There is a clear need for such an analysis, since any discussion about non-stationarity 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 local consistency and asymptotic normality are established as well.