STATISTICAL THEORY FOR HIGHER ORDER NONSTATIONARY INTEGRATED AND COINTEGRATED PROCESSES
Project/Area Number  05630012 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
Economic statistics

Research Institution  HITOTSUBASHI UNIVERSITY 
Principal Investigator 
TANAKA Katsuto HITOTSUBASHI UNIVERSITY,PROFESSOR, 経済学部, 教授 (40126595)

Project Fiscal Year 
1993 – 1994

Project Status 
Completed(Fiscal Year 1994)

Budget Amount *help 
¥2,000,000 (Direct Cost : ¥2,000,000)
Fiscal Year 1994 : ¥300,000 (Direct Cost : ¥300,000)
Fiscal Year 1993 : ¥1,700,000 (Direct Cost : ¥1,700,000)

Keywords  INTEGRATED PROCESS / COINTEGRATION / ASYMPTOTIC THEORY / BROWNIAN MOTION / LOCAL ALTERNATIVE / 和分過程 / 共和分関係 / 漸近理論 / ブラウン運動 / 局所対立仮説 / 非定常過程 / 共和分 
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.

Report
(4results)
Research Output
(15results)