On a Non-linear Risk Analysis for Stock Market Indexes |
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| Authors: | Kenjiro Suzuki Yasunori Okabe Takaaki Fujii |
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| Institution: | (1) Mitsubishi Research Institute Inc. 3–6, Otemachi 2-Chome, 100-8141 Chiyoda-ku, Tokyo, Japan;(2) Department of Mathematics, School of Science and Technology, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasakishi 214-8571, Japan;(3) Aioi Insurance Co. Ltd., 1-28-1, Ebisu, Shibuya-ku, Tokyo 150-8488, Japan |
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| Abstract: | We propose a method to detect early signs of a potential major crash in the market from only the information of the time series
representing its stock market data. As reinforcement of the abnormality test Test(ABN) developed in Okabe, Matsuura, and Klimek
(International Journal of Pure and Applied Mathematics, 3, 443–484, 2002), we introduce in this paper a risk graph to measure abnormality of time series by using the non-linear prediction
analysis in the theory of KM2O-Langevin equations. By applying it to real data of stock market indexes on the Black Monday of 1987 and those during the
past 7 years from January 2000 to December 2006, we investigate whether we can detect early signs of a potential major crash
in the market by watching the behavior of the risk graph.
An erratum to this article can be found at |
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| Keywords: | Stock market crashes KM2O-Langevin equation Test(ABN) Abnormality graph Stationarity graph Risk graph |
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