On location estimation for LARCH processes

We consider location estimation when the error process is a stationary LARCH process with long memory in the second moments. The asymptotic distribution of the sample mean and nonlinear M -estimators of the location parameter are derived. Essential assumptions for obtaining asymptotic normality with n - 1 2 -rate of convergence are symmetry of the innovation distribution and skew-symmetry of the ψ -function.