9730295 Phillips This project is concerned with modelling, estimation and inference for nonstationary economic data. It consists of three parts: nonlinear and nonparametric analysis for integrated time series data, panel cointegration analysis, and spurious regression analysis. Each part involves theoretical research and empirical applications. Nonstationary time series arising from autoregressive models with roots on the unit circle have been an intensive study of econometric research in the last decade and there is now a fairly complete theory available for linear time series regressions. As in other regression contexts, linear models can be restrictive and they eliminate many interesting cases of practical importance where there are nonlinear responses. This project provides the first systematic study of time series with unit root or near unit root nonstationarity to nonlinear regression, kernel regression and nonparametric density estimation contexts. The work involves new methodological developments that utilize discrete time estimates of the local time for continuous stochastic processes such as Brownian motion, i.e., the occupation density for the time spent by the process in the spatial vicinity of a certain part. This quantity turns out to be important in analyzing nonlinear functions of nonstationary data and in the development of an asymptotic theory of nonlinear regression. The second part is concerned with the development of a regression limit theory and associated inferential methods for nonstationary panel data sets with large numbers of cross section and time series observations. Several interesting panel structures are possible allowing, for instance, for no time series cointegration, heterogeneous cointegration, homogeneous cointegration, or even near-homogeneous cointegration. Since panel data can distinguish effects that time series of cross section data alone cannot identify, there are exciting possibilities for the use of such methods in studying imp ortant empirical economic issues such as the growth convergence where nonstationary data can play a central role. The third part continues the investigator's work on spurious regression. His earlier work helped to explain "spurious" statistical significance in regression by the development of an asymptotic theory of the regression. More recently, the investigator has shown than an alternative asymptotic theory can be developed that justifies the same regression in terms of the representation of one function (possibly, stochastic function) in terms of others. In this project these tools of analysis will be extended to develop a theory of approximating regression functions, including approximately cointegration functions, and to develop an associated inferential theory. ??
