Higher Moments and Prediction-Based Estimation for the COGARCH(1,1) Model

COGARCH models are continuous time versions of the well-known GARCHmodels of financial returns. The first aim of this paper is to show how the method of prediction-based estimating functions can be applied to draw statistical inference from observations of a COGARCH(1,1) model if the higher-order structure of the process is clarified. A second aim of thepaper is to provide recursive expressions for the joint moments of any fixed order of the process.Asymptotic results are given, and a simulation study shows that the method of prediction-basedestimating function outperforms the other available estimation methods.