This project proposes to tackle several very important and difficult issues in modeling general climatological, economic and financial time series data involving possible deterministic and stochastic trending components. This project seeks to establish some general asymptotic theory for model identification and estimation technologies that are suited to such general trending time series data that may be stochastically nonstationary and endogeneous. The research outcomes of this project are expected to make significant contributions to the literature as well as to be applicable in evaluating and improving empirical models used in climatology, economics, environmetrics and financial econometrics with possible endogeneity and nonstationarity.