Multiple Structural Changes with Deterministic and Stochastic Trends

在之前的工作中，我们提供了与线性模型中具有平稳或确定性趋势变量的多个结构变化相关的问题的综合处理。该建议解决了与经验重要情况下的多个结构变化相关的问题，其中单个变量可能是整合的，变量系统可能是协整的。积分变量的存在需要一个完全不同的理论装置，并且在采用测试策略时造成严重困难。这是因为极限分布取决于单位根是否存在，但与此同时，关于单位根存在的推论取决于结构变化是否存在。因此，需要采取联合措施。要解决的问题将是新的理论结果以及更实际的方面，包括对有限样本中程序的充分性的广泛模拟。该研究将分析给定趋势函数斜率变化的单变量积分序列估计断裂日期的一致性。这将产生更强大的过程，因为可以使用与已知中断日期相对应的临界值来测试单位根。计划中的研究包括开发检验单变量时间序列趋势函数结构变化的方法，无论是否存在单位根，这种方法都有效。对于多变量情况，研究将解决断点估计的一致性（无论是在确定性成分还是协整向量中）；结构变化存在的检验与协整向量的数量无关；并检验允许多重结构变化的协整向量的数量。在这种多变量情况下，我们打算推广单变量修正AIC来选择滞后长度。最后，我们打算开发一种有效的估计程序，在这种情况下，其他方法来构建断裂日期的估计将失效。在所有的研究课题中，我们打算为应用研究人员提供一套全面的工具，所有的程序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.