ABSTRACT
A fairly general approach to characterizing the robustness properties of estimators in the time series context was given by R. D. Martin and V. J. Yohai. They considered an influence functional for the so-called general replacement model. Long memory is characterized by the behavior of the spectral density at the origin. For simple models such as fractional Gaussian noise or a fractional ARIMA process, this is a good approximation even for large frequencies. Fitting these models therefore basically amounts to fitting a straight line to the periodogram in log-log coordinates. One of the typical features of stationary long-memory processes is that there appear to be local trends and cycles, which are, however, spurious and disappear after some time. This property can make it rather difficult to distinguish a stationary process with long memory from a non-stationary process. Sometimes, additional, possibly non-numerical, information is available that favors either non-stationarity or stationarity.
