1990 Fiscal Year Final Research Report Summary
Statistical Theory and Application of Nonstationary and Noninvertible Time Series Model
| Project/Area Number |
01530014
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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 |
統計学
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| Research Institution | Hitostubashi 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) |
1989 – 1990
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| Keywords | Nonstationary Process / Noninvertibility / Random Walk / Time Series Model |
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| Research Abstract |
There are three major results of the present research. The first is the construction of a unified approach to the asymptotic theory of statistics associated with nonstationary time series models. For nonstationary time series models we suggested a general approach to computing accurately the limiting distribution of the statistic of a ratio of quadratic and bilinear forms in random variables. The traditional approach based on invariance principles is unable to do this. One just has to rely on simulations, while the present approach approach overcame that ambiguity.
Second we explored asymptotic properties of the maximum likelihood estimator for the noninvertible moving average model. In comparison with autoregressive models the analysis in much harder with moving average models. We attempted to derive the limiting distribution of the maximum likelihood estimator, but in vein. On the other hand we suggested testing for a moving average unit root, which contains some interesting results.
Third an asymptotic theory of cointegration has been developed. Cointegration is now the most important topic in the area of nonstationary time series analysis. We derived the asymptotic distribution of the least squares estimator of the cointegrating vector. It is only recently that I noticed that cointegration is closely connected with noninvertibility of moving average models. I also realized that cointegration can be tested in terms of invertibility of the moving average model, which will be a topic for future research.
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