1994 Fiscal Year Final Research Report Summary
STATISTICAL THEORY FOR HIGHER ORDER NONSTATIONARY INTEGRATED AND COINTEGRATED PROCESSES
| Project/Area Number |
05630012
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
Economic statistics
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| Research Institution | HITOTSUBASHI UNIVERSITY |
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Principal Investigator |
TANAKA Katsuto HITOTSUBASHI UNIVERSITY,PROFESSOR, 経済学部, 教授 (40126595)
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| Project Period (FY) |
1993 – 1994
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| Keywords | INTEGRATED PROCESS / COINTEGRATION / ASYMPTOTIC THEORY / BROWNIAN MOTION / LOCAL ALTERNATIVE |
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| Research Abstract |
The present research has extended over two years. I first describe the results obtained each year and then give perspectives for further research.
1.1993
I 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.
2.1994
A 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.
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