  Three long memory models, ARFIMA, Timmer and Konig 1995, and a circular
convolution model based on Wold's representation theorem are examined. Each
model is shown to produce sequences with nonstationary generalized beta
marginal distributions. It is demonstrated that the variance divided by the
squared range of the sequence is stationary, and is a function of the shape
parameter of the resulting symmetric beta distribution. Using the Wold model, a
simple matrix distribution transformation is given that maps the normal
components of the long memory model onto the beta distribution.
