Modelling nonlinearity and long memory in time series

We discuss models that impart a form of long memory in raw time series xt or instantaneous functions thereof, in particular . on the basis of a linear or nonlinear model. The capacity of linear models for xt to imply long-memory in nonlinear functions of xt is discussed. Empirical observation motivates investigation of models which lead to short memory, or even white noise, xt but a long memory . One such model which we describe is based on the long memory generalized ARCH model introduced by Robinson (1991b). The other is an extension of the nonlinear moving average model of Robinson (1977).