On a Non-linear Risk Analysis for Stock Market Indexes

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.