COGARCH models: some applications in finance

COGARCH models are continuous time version of the well known GARCH models of financial returns. The aim of this paper is to show how the method of Prediction-Based Estimating Functions can be applied to estimate the parameters of a COGARCH(1,1) model from observations taken from real data set. In particular the General Motors tick-by-tick data of the Trades and Quotes database of the New York Stock Exchange (NYSE) are considered. A comparison between the results obtained with the method of moments estimator is done in terms of stability of the estimates over different windows of observations and in terms of analysis of residuals.