2006 Fiscal Year Final Research Report Summary
Characteristics of Critical Fluctuations Caused by Self-Modulation and its Application
| Project/Area Number |
16540346
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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 |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
TAKAYASU Misako Tokyo Institute of Technology, Interdisciplinary Graduate School of Science and Technology, Department of Computational Intelligence and Systems Science, Associate Professor, 大学院総合理工学研究科, 助教授 (20296776)
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| Project Period (FY) |
2004 – 2006
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| Keywords | Self-Modulation / Data Analysis / Stochastic Process / Autocorrelation / Optimal Moving Average / Market Price Fluctuations |
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| Research Abstract |
I analyzed so-called the self-modulation systems which are dynamical stochastic processes whose parameters are given by the moving averages of their own traces. In these 3 years I have studied the basic properties and also applications.
The most typical example of the self-modulation systems is the transaction intervals in open markets such as the Yen-Dollar exchange market. I have shown that the time sequence of the intervals normalized by an optimal moving average is quite well approximated by a pure Poisson process. Here, the optimal moving average is given by a weighted moving average with exponential decay of characteristic time about 30 seconds.
Then the basic idea of self-modulation is generalized to the market prices especially to the Yen-Dollar market which I have the high quality data for more than 10 years. I firstly introduced an optimal moving average for the market prices and then observed the dynamics of this noise-reduced market price. It is found that the dynamics is not purely random as assumed by the financial technology, I found clear evidence that there exists a potential force of market. This potential force is not a constant but its center is moving with a larger scale moving average and the curvature of the potential is also changing slowly between a positive stable state to a negative unstable state. This dynamical property can be characterized by the potential coefficient. As this analysis is suitable for risk evaluation of markets, I developed a real time data analysis algorithm which is ready to be applied to the real open market.
It is also shown theoretically that the potential force formulation is expressed as a kind of self-modulation process for the price difference, so the applicability of the self-modulation has been enlarged considerably.
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