Long memory or shifting means in geophysical time series?

In the literature many papers state that long-memory time series models such as Fractional Gaussian Noises (FGN) or Fractionally Integrated series (FI(d)) are empirically indistinguishable from models with a non-stationary mean, but which are mean reverting. We present an analysis of the statistical cost of model mis-specification when simulated long memory series are analysed by Atheoretical Regression Trees (ART), a structural break location method. We also analysed three real data sets, one of which is regarded as a standard example of the long memory type. We find that FGN and FI(d) processes do not account for many features of the real data. In particular, we find that the data sets are not H-self-similar. We believe the data sets are better characterized by non-stationary mean models.