Quasi maximum likelihood estimation and prediction in the compound Poisson ECOGARCH(1,1) model

This paper deals with the problem of estimation and prediction in a
compound Poisson ECOGARCH(1,1) model. For this we construct a quasi
maximum likelihood estimator under the assumption that all jumps of
the log-price process are observable. Since these jumps occur at
unequally spaced time points, it is clear that the estimator has to
be computed for irregularly spaced data. Assuming normally
distributed jumps and a recursion to estimate the volatility allows
to define and compute a quasi-likelihood function, which is
maximised numerically. The small sample behaviour of the estimator
is analysed in a small simulation study. Based on the recursion for
the volatility process a one-step ahead prediction of the
volatility is defined as well as a prediction interval for the
log-price process. Finally the model is fitted to tick-by-tick data
of the New York Stock Exchange.