Varying coefficient partially nonlinear models with nonstationary regressors

We study a varying coefficient partially nonlinear model in which the regressors are generated by the multivariate unit root processes. A profile nonlinear least squares estimation procedure is applied to estimate the parameter vector and the functional coefficients. Under some mild conditions, the asymptotic distribution theory for the resulting estimators is established. The rate of convergence for the parameter vector estimator depends on the properties of the nonlinear regression function. However, the rate of convergence for the functional coefficients estimator is the same and enjoys the super-consistency property. Furthermore, a simulation study is conducted to investigate the finite sample performance of the proposed estimating procedures. •A varying coefficient partially nonlinear model with nonstationary regressors model is considered.•A profile nonlinear least squares estimation method is used to estimate the parameter vector and the functional coefficients.•The asymptotic convergence results for both the parametric and nonparametric estimators are established under mild conditions.•Our asymptotic results substantially generalize the existing results concerning the nonlinear nonstationary regression models.