Asymptotic behaviour of the LS estimator in a nonlinear model with long memory

The behaviour of the LS estimator in a nonlinear regression model is investigated, when both the regressors and the errors are long memory processes. The convergence rate, the asymptotic distribution of the LS estimator depend on long memory parameters, Hermite ranks and on expectation of the partial derivative with respect to the parameter of the regression function. We show that the asymptotic distribution of this estimator can be non-normal. An application of these results is presented for testing a structural change in a model with change-point. Numerical simulations confirm the theoretical results.