Simultaneous Confidence Bands in Nonlinear Regression Models with Nonstationarity

We consider nonparametric estimation of the regression function g(*) in a nonlinear regression model Y_t = g(X_t) o(X_t)e_t, where the regressor X_t is a nonstationary unit root process and the error e_t is s sequence of independent and identically distributed (i.i.d.) random variables. With proper centering and scaling, the maximum deviation of the local linear estimator of g is shown to be asymptotically Gumbel. Based on the latter result, we construct simultaneous confidence bands for g, which can be used to test patterns of the regression function g. Our results substantially extend existing ones which typically require independent or stationary weakly dependent regressors. Furthermore, we provide a simulation study to illustrate the finite sample behavior of the proposed approach