Nonlinear cointegrating regressions with nonstationary time series

Nigel Chan and Qiying Wang

Abstract

This paper develops an asymptotic theory for a non-linear parametric co-integrating regression model. We establish a general framework for weak consistency that is easy to apply for various non-stationary time series, including partial sum of linear process and Harris recurrent Markov chain. We provide a limit distribution for the nonlinear least square estimator which significantly extends the previous work. We also introduce endogeneity in the model by allowing the error to be serially dependent and cross correlated with the regressor.

Keywords: Cointegration, nonlinear regression, consistency, limit distribution, nonstationarity, nonlinearity, endogeneity.

AMS Subject Classification: Primary 62G05;; secondary 62G20.