Large-Sample Properties of Parameter Estimates for Strongly Dependent Stationary Gaussian Time Series

This is the authors' abstract. We don't add key points for this paper.

A strongly dependent Gaussian sequence has a spectral density f(x, θ) satisfying f(x, θ) ~ |x|-α(θ) L_θ(x) as x → 0, where 0 < α(θ) < 1 and L_θ(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.