Gaussian inference on certain long-range dependent volatility models

For a class of long memory volatility models, we establish the asymptotic distribution theory of the Gaussian estimator and the Lagrange multiplier test. Both the case of estimation of martingale difference and ARMA levels are considered. A Monte Carlo exercise is presented to assess the small sample properties of the Gaussian estimator and the Lagrange multiplier test. An empirical application, using foreign exchange rates and stock indexes returns, suggests the potential of these models to capture the dynamic features of the data.