Maximum Quasi-likelihood Estimation in Fractional Levy Stochastic Volatility Model

Abstract

Usually asset price process has jumps and volatility process has long memory. We study maximum quasi- likelihood estimators for the parameters of a fractionally integrated exponential GARCH, in short FIECO- GARCH process based on discrete observations. We deal with a compound Poisson FIECOGARCH process and study the asymptotic behavior of the maximum quasi-likelihood estimator. We show that the resulting estimators are consistent and asymptotically normal.