ON M-Estimation Under Long-Range Dependence in Volatility

Abstract.  We consider M-estimation of a location parameter for processes with zero autocorrelations but long-range dependence in volatility. The observed process is the product of i.i.d. Gaussian observations and a long-memory Gaussian process. For nonlinear estimators, the rate of convergence depends on the type of the ψ-function. For skew-symmetric ψ-functions, a central limit theorem with -rate of convergence holds, under suitable regularity assumptions. This is not true in general for M-estimators where the ψ-function is not skewsymmetric.