Nonstationary Economic Time Series and Panel Data

9730295 Phillips这个项目涉及非平稳经济数据的建模、估计和推断。它包括三个部分：集成时间序列数据的非线性和非参数分析、面板协整分析和伪回归分析。每个部分都涉及理论研究和实证应用。由单位圆上有根的自回归模型引起的非平稳时间序列是近十年来计量经济学研究的热点，目前已有比较完整的线性时间序列回归理论。正如在其他回归环境中一样，线性模型可能是限制性的，并且它们消除了许多具有实际重要性的有趣情况，其中存在非线性响应。该项目首次系统地研究了非线性回归、核回归和非参数密度估计背景下具有单位根或近单位根非平稳性的时间序列。这项工作涉及新的方法发展，利用离散时间估计连续随机过程的局部时间，如布朗运动，即过程在某一部分的空间附近所花费的时间的占用密度。这个量在分析非平稳数据的非线性函数和发展非线性回归的渐近理论中是很重要的。第二部分关注具有大量横截面和时间序列观测的非平稳面板数据集的回归极限理论和相关推理方法的发展。一些有趣的面板结构可能允许，例如，无时间序列协整，异质协整，齐次协整，甚至是近齐次协整。由于面板数据可以区分单独的时间序列横截面数据无法识别的影响，因此在研究重要的实证经济问题（如非平稳数据可以发挥核心作用的增长收敛）时，使用此类方法具有令人兴奋的可能性。第三部分继续研究者对伪回归的研究。他早期的工作通过发展渐近回归理论，帮助解释了回归中的“虚假”统计显著性。最近，研究者已经证明了可以开发出一种替代渐近理论，该理论可以根据一个函数（可能是随机函数）的表示来证明相同的回归。在这个项目中，这些分析工具将扩展到发展近似回归函数的理论，包括近似协整函数，并发展相关的推理理论。？?

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. ??