Testing for Unit Roots and Cointegration Using Covariates

在应用计量经济学中研究时间序列性质最常用的模型是“单位根模型”。协整模型是对单变量单位根的多元推广，它允许有共同的单位根分量。在大多数应用中，对单位根或协整的检验被视为建立经验模型的有用的初步步骤。但在许多情况下，协整作为一个经济模型的含义出现，协整检验可以用来直接检验模型。例子包括生命周期模型、股票价格的现值模型、实际商业周期模型、利率期限结构模型、跨期消费模型和长期货币需求函数的研究。但是单位根和协整检验不能用于许多经济应用，因为考虑到经济数据中可获得的典型观察数量，它们不足以区分相互竞争的假设。本项目开发了一种利用传统方法所忽略的信息来显著提高单位根和协整检验幂的方法，并将该方法推广到所有情况，使用局部到单位渐近技术来研究有限样本中渐近逼近的充分性，并重新检查Nelson- Plosser数据集，以查看改进的检验是否可以揭示序列的随机性质。

9412339 Hansen The most common model used in applied econometrics to study the properties of time series is the "unit root model." A multivariate generalization of univariate unit roots which allows for common unit root components is the model of cointegration. In most applications, testing for unit roots or cointegration are viewed as useful preliminary steps in the building of an empirical models. But in many cases, cointegration emerges as an implication of an economic model and cointegration tests can be used to directly test the model. Examples include studies of the life-cycle model, the present value model of stock prices, real business cycle models, models of the term structure of interest rates, a model of intertemporal consumption, and the long-run money demand function. But unit root and cointegration tests can not be used for many economic applications because they are not powerful enough to discriminate among competing hypotheses given the typical number of observations available in economic data. This project develops a method for increasing the power of unit root and cointegration tests dramatically by using information that is ignored by more conventional methods, generalizes this method to all cases, uses the technique of local-to-unity asymptotics to investigate the adequacy of the asymptotic approximations in finite samples, and reexamines the Nelson- Plosser data set to see if the improved tests can shed light on the stochastic properties of the series.