STATISTICAL THEORY FOR HIGHER ORDER NONSTATIONARY INTEGRATED AND COINTEGRATED PROCESSES

目前的研究已经持续了两年多。我首先描述了每年获得的结果，然后给出了进一步研究的观点。我分析了一个时间序列回归模型，其中回归量是非平稳的，并且遵循综合过程。特别地，研究了积分阶大于1的过程的统计量，并求出了它们的极限分布。对于这样高阶的积分过程，在数值计算上是很难处理的，但是我设计了一种方法来克服这个困难。另一方面，我发现积分阶为1的情况在分布理论中是非常特殊的，可以说，它对应于一个奇异点。2.1994一个新的检验程序，用于检验高度非平稳变量之间是否存在协整。传统检验以无协整为零，而建议检验以协整为零。我不仅导出了极限零，而且还导出了局部替代序列下的极限分布。并计算相应的百分点。在以上和其他结果的基础上，我可以在项目期间写一篇手稿，即将发表。为了进一步研究，我想提出一种方法，使我们能够处理比本项目分析的统计数据更复杂的统计数据。当然，要像在标准情况下那样做是困难的，但我将努力找到这个扩展问题的线索。

The present research has extended over two years. I first describe the results obtained each year and then give perspectives for further research.1.1993I analyzed a time series regression model, where the regressors are highly nonstationary and follow integrated processes. In particular statistics arising from processes of integration order greater than 1 are studied, and their limiting distributions are found and computed. In terms of numerical computation it is hard to deal with such higher order integrated processes, but I have devised a method for overcoming such difficulties. On the other hand I have found that the case of integration order of 1 is quite exceptional in terms of distribution theory, which corresponds, so to speak, to a singular point.2.1994A new testing procedure for testing if there exists cointegration among highly nonstationary variables. While conventional tests take no cointegration as the null, the suggested test takes cointegration as the null. I have derived, not only the limiting null, but also the limiting distributions under a sequence of local alternatives. The corresponding percent points are also computed.3. On the basis of the above and other results I could write a manuscript during the term of project, which is to be published shortly. For further research I would like to suggest a method which enables us to deal with more complicated statistics than those analyzed in the present project. It is certaily difficult to do so as in the standard case, but I will try to find a clue to this extended problem.