On Model Approximation for Long-Memory
Processes: A Cautionary Result

An Essay in Honor of Professor
G. S. Maddala

Clive W. J.
Granger

It is pointed out that if the generating mechanism is a fraction
integrated process I(d), where d can be less than 1/2, but a simple ARMA
model is fitted, a consistent estimation procedure is likely to produce a
unit root. Thus the properties of the fitted model will be quite unlike those of the generating mechanism.