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

An Essay in Honor of Professor G. S. Maddala

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.