This chapter reviews semiparametric methods of inference on different aspects of long memory
time series. The main focus is on estimation of the memory parameter of linear models, analyzing
bandwidth choice, bias reduction techniques and robustness properties of different estimates, with
sorne emphasis on nonstationarity and trending behaviors. These techniques extend naturally to multivariate series, where the important issues are the estimation of the long-run relationship and
testing for fractional cointegration. Specific techniques for the estimation of the degree of persistence
of volatility for nonlinear time series are also considered