2004 Fiscal Year Final Research Report Summary
A study of Ihigher-ooder moment long-range dependence in economic time-series
| Project/Area Number |
15530136
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Economic statistics
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| Research Institution | Tohoku University |
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Principal Investigator |
HOSOYA Yuzo Tohoku University, Graduate School of Economics and Management, Professor, 大学院・経済学研究科, 教授 (40004197)
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| Project Period (FY) |
2003 – 2004
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| Keywords | long-range dependency / conditional heteroscedasticity / higher-order cumulant / cumulant spectrum / cointeration / statistical asymptotic theory / Whittle likelihood |
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| Research Abstract |
In the 2003-2004 research, a basic theoretical framework was developed to deal with statistical inference on higher-order moment dependency of stationary time-series data and also developed a set of algorithm for numerical computation. The approach for this purpose is to apply statistical inference theory of second-order multivariate stationary processes to the joint process consisting of the series in question and its squared series. By this method, we are able to model the second, third and fourth-order serial dependency. In order to accommodate long-range dependency, the Whittle likelihood in the frequency-domain representation is appropriate. The asymptotic estimation and testing theory of the Whittle likelihood is applicable under suitable modification. To deal with nonlinear multivariate processes of long range dependency, this research investigated the fractional cointegrated model which extends the Johansen's unit-root cointegration model and its properties. Also a version of functional central limit theorem was established on type 2 fractional Brown motion and the asymptotic distribution of the Whttle likelihood ratio statistic for the cointegration rank was derived. Higher-order moment dependency is closely related to non-Gaussianity of a process in concern. Another approach to deal with such non-Gaussianity is to transform nonlinearly the process. For that purpose, a model of modified Box-Cox transformation ARMA is investigated in this research and an asymptotic theory is developed.
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