Large-sample properties of parameter estimates for strongly dependent stationary gaussian time series

A strongly dependent Gaussian sequence has a spectral density f(x,θ) satisfying f(x,θ)∼|x|−α(θ)Lθ(x) as x→0, where 0<α(θ)<1 and Lθ(x) varies slowly at 0. Here θ is a vector of unknown parameters. An estimator for θ is proposed and shown to be consistent and asymptotically normal under appropriate conditions. These conditions are satisfied by fractional Gaussian noise and fractional ARMA, two examples of strongly dependent sequences.