Estimators for alternating nonlinear autoregression

Suppose we observe a time series that alternates between different nonlinear autoregressive processes. We give conditions under which the model is locally asymptotically normal, derive a characterization of efficient estimators for differentiable functionals of the model, and use it to construct efficient estimators for the autoregression parameters and the innovation distributions. Surprisingly, the estimators for the autoregression parameters can be improved if we know that the innovation densities are equal.