Multiple Structural Changes with Deterministic and Stochastic Trends

在以前的工作中，我们提供了一个全面的处理问题的线性模型与固定或确定性趋势变量的多个结构变化。这一建议涉及的问题，多个结构变化的经验重要的情况下，个别变量可能是一体化的，一个系统的变量可能是协整。 综合变量的存在需要一个完全不同的理论装置，并在测试策略中提出了严重的困难。这是因为极限分布取决于是否存在单位根，但同时，关于单位根存在的推断取决于是否存在结构变化。因此，需要采取联合办法。要解决的问题将是新的理论结果，以及更实际的方面，包括广泛的模拟程序在有限样本的充分性。该研究将分析的一致性，估计休息日期的变化趋势函数的一个单变量综合系列。这是预期产生更强大的程序，因为在ecan然后测试单位根使用临界值对应的情况下，一个已知的突破日期。计划中的研究包括对一个单变量时间序列的趋势函数的结构变化进行测试，无论单位根是否存在，这些测试都是有效的。 对于多变量的情况下，研究将解决的断点估计的一致性（无论是在确定性的组件或协整向量）;测试的结构变化的存在是不可知的协整向量的数量;和测试的协整向量的数量允许多个结构变化。在这种多变量的情况下，我们打算推广单变量修改AIC的滞后长度的选择。 最后，我们打算开发一种有效的估计程序，以应对其他构建中断日期估计的方法将失败的情况。在所描述的所有研究主题中，我们打算为应用研究人员提供一套全面的工具，并且所有程序都将在高斯程序中提供，该程序将根据要求分发。

In previous work, we provided a comprehensive treatment of issues related to multiple structural changes in the linear model with stationary or deterministically trending variables. This proposal addresses issues related to multiple structural changes for the empirically important cases where the individual variables are possibly integrated and a system of variables is possibly cointegrated. The presence of integrated variables requires a drastically different theoretical apparatus and poses serious difficulties in the testing strategies to be adopted. This is due to the fact that the limit distributions depend on whether or not a unit root is present but, at the same time, inference about the presence of a unit root depends on whether structural changes are present. Hence, a joint approach is needed. The issues to be tackled will be new theoretical results as well as more practical aspects including extensive simulations about the adequacy of the procedures in finite samples. The research will analyze the consistency of estimated break dates given changes in the slope of a trend function for a univariate integrated series. This is expected to yield more powerful procedures since on ecan then test for a unit root using critical values corresponding to the case of a known break date. The planned research includes the development of tests for structural changes in the trend function of a univariate time series that are valid whether a unit root is present or not. For the multivariate case, research will address the consistency of the break point estimates (whether in the deterministic components or the cointegration vectors); tests for the presence of structural change being agnostic about the number of cointegrating vectors; and tests for the number of cointegrating vectors allowing for multiple structural changes. In this multivariate case, we intend to generalize the univariate Modified AIC for choice of lag length. Finally, we intend to develop an efficient estimation procedure for cases in which other methods for constructing estimates of the break dates will break downIn all the research topics described, we intend to provide applied researchers with a comprehensive set of tools and all procedures will be made available in a Gauss program that will be distributed on request.