Simultaneous confidence bands for time-series prediction function

Although many types of confidence bands exist for nonparametric regression with i.i.d. data, theoretical properties of such bands have never been established under dependence. We propose simultaneous confidence bands for nonparametric prediction function of time-series data using spline estimation. Asymptotic properties are established under the assumption of strong mixing, and simulation experiments have provided strong evidence that corroborates with the asymptotic theory. As an application, after removing the environmental Kuznets curve trend effects, the impact of the economic intervention on environmental quality change is quantified for the USA and Japan, with different conclusions.