Nonlinear regressions with nonstationary time series

This paper develops asymptotic theory for a nonlinear parametric cointegrating regression model. We establish a general framework for weak consistency that is easy to apply for various nonstationary time series, including partial sums of linear processes and Harris recurrent Markov chains. We provide limit distributions for nonlinear least square estimators, extending the previous works. We also introduce endogeneity to the model by allowing the error to be serially dependent on and cross correlated with the regressors.