Essays on nonstationary nonlinear time series models

In empirical studies, practitioners routinely adopt linear models as approximations to complicated economic relations. Linear models are helpful in substantive economic problems. Ignoring nonlinear features, however, can sometimes be misleading for policymakers. To understand the complexity of the real world, simple, interpretable nonlinear models are advantageous. To this end, this research have developed multiple statistical methods for time series data with nonlinearity and non-stationarity. The study mainly considered two sets of models. The first set is called trend-break models that allow a structural break in the time trend, possibly due to changes in policy or external events, without the information of break dates to modelers. The dissertation proposes a framework to pin down the break dates and quantify the estimation uncertainty. The second set is the co-integrating polynomial regression models. It is motivated mainly by the environmental Kuznets curve hypothesis that postulates an inverse U-shaped relationship between per capita income and environmental degradation. The study offers some statistical methods to assess this hypothesis carefully.