Recent Developments in Location Estimation and Regression for Long-Memory Processes

The problem of long-range dependence in statistical applications has been known to scientists and applied statisticians long before suitable models were known. Parsimonious models with such behaviour are stationary processes with non-summable correlations. Many classical limit theorems do not hold for these processes and rates of convergence are slower than under independence or weak dependence. Therefore, for many statistics, usual confidence intervals are too small by a factor which tends to infinity with increasing sample size. In this paper we give a survey of recent results on point and interval estimation of location and of the coefficients in parametric linear regression, as well as nonparametric regression.