Invariance principles for fractionally integrated nonlinear processes
  We obtain invariance principles for a wide class of fractionally integrated nonlinear processes. The limiting distributions are shown to be fractional Brownian motions. Under very mild conditions, we extend earlier ones on long memory linear processes to a more general setting. The invariance principles are applied to the popular R/S and KPSS tests. 
Wei Biao Wu, Xiaofeng Shao