Nonlinear models with strongly dependent processes and applications to forward premia and real exchange rates

This paper considers estimation and inference in some general non linear time series models which are embedded in a strongly dependent, long memory process. Some new results are provided on the properties of a time domain MLE for these models. The paper also includes a detailed simulation study which compares the time domain MLE with a two step estimator, where the Local Whittle estimator has been initially employed to filter out the long memory component. The time domain MLE is found to be generally superior to two step estimation. Further, the simulation study documents the difficulty of precisely estimating the parameter associated with the speed of transition. Finally, the fractionally integrated, nonlinear autoregressive-ESTAR model is found to be extremely useful in representing some financial time series such as the forward premium and real exchange rates.