A Smooth Transition Long-Memory Model

This paper proposes a new fractional model with a time-varying long-memory parameter. The latter evolves nonlinearly according to a transition variable through a logistic function. We present a LR-based test that allows to discriminate between the standard fractional model and our model. We further  apply the nonlinear least squares method  to estimate the long memory parameter. We present an application to the unemployment rate in the United-States from 1948 to 2012.