A fractionally integrated ECOGARCH process

In this paper we introduce a fractionally integrated exponential
continuous time GARCH(p,d,q) process. It is defined in such a way
that it is a continuous time extension of the discrete time
FIEGARCH(p,d,q) process. We investigate stationarity and moment
properties of the new model. It is also shown that the long memory
effect introduced in the log-volatility propagates to the
volatility process.