This project encompasses four distinct, but interrelated areas of research in probabilistic functional limit theory. They are: (1) optimal tests of parameter constancy, (2) median unbiased estimation and confidence interval construction for nonstationary time series, (3) empirical process limit theory for dependent non-identically distributed random variables, and (4) semiparametric econometric methods. The results of this research will provide powerful, new tools for applied economic analysis including research on the economics of global environmental change. The proposed work on parameter constancy covers tests of structural change with an unknown change point and tests of regime switching. This part of the project is important because there currently are no asymptotically optimal tests available for testing for parameter constancy when the standard regularity conditions fail. The proposed research on median unbiased estimation and confidence interval construction is significant because current tests have low power. The new tools developed under this project can be used to provide analysts more information for the types of time series problems that are frequently encountered in empirical economics. The basic limit results for dependent non-identically distributed random variables also have applications in a wide variety of time series econometric problems. In the fourth area of research the project develops tests for heteroskedasticity, autocorrelation, asymptotic normality for semiparametric and nonparametric estimators. Semiparametric estimators are widely used by economists because the data for many economic problems do not fit the assumptions required for standard parametric analysis and these new tests can be used for a very wide range of semiparametric estimators. These methods are especially appropriate for the type of forecasting and empirical analytical problems encountered in the economics of global change because of the poor quality of the data, the uncertainty about many of the underlying economic relationships, and the possibility of changes in the structure of the economic system being studied.
