This paper shows that the properties of nonlinear transformations of a fractionally integrated process depend strongly on whether the initial series is stationary or not. Transforming a stationary Gaussian I(d) process with d 0 leads to a long-memory process with the same or a smaller...

This paper shows that the properties of nonlinear transformations of a fractionally integrated process depend strongly on whether the initial series is stationary or not. Transforming a stationary Gaussian I(d) process with d 0 leads to a long-memory process with the same or a smaller...

A frequent property of data, particularly in the financial area, is that the correlogram is low but remains positive for many lags. A plausible explanation for this is that the process consists of a stationary, long memory component plus a white noise component of much larger variance. The...