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STATISTICAL THEORY FOR HIGHER ORDER NONSTATIONARY INTEGRATED AND COINTEGRATED PROCESSES

高阶非平稳综合与协整过程的统计理论

基本信息

批准号：
05630012
负责人：
TANAKA Katsuto
金额：
$ 1.28万
依托单位：
HITOTSUBASHI UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1994
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05630012/
关键词：
INTEGRATED PROCESS COINTEGRATION ASYMPTOTIC THEORY BROWNIAN MOTION LOCAL ALTERNATIVE 非定常過程共和分

项目摘要

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.

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，然后给出进一步研究的前景。1.1993我分析了一个时间序列回归模型，其中回归量是高度非平稳的，并遵循综合过程。特别是统计所产生的过程中的集成顺序大于1进行了研究，并发现和计算其极限分布。在数值计算方面，很难处理这样的高阶积分过程，但我已经设计了一种方法来克服这些困难。另一方面，我发现，1的集成顺序的情况下是非常例外的分布理论，这对应于，可以这么说，一个奇异点。2.1994年一个新的测试程序，用于测试，如果存在高度非平稳变量之间的协整。传统的检验将不存在协整作为空值，而建议的检验将协整作为空值。我不仅导出了极限零点，而且还导出了在一个局部选择序列下的极限分布。也计算了相应的百分点。在上述和其他结果的基础上，我可以在项目期间写一份手稿，不久将出版。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中分析的更复杂的统计数据。在标准情况下，这样做肯定很困难，但我将试图找到这个扩展问题的线索。