# Q ： How to predict the crash of individual firms?.

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Q ： How to predict the crash of individual firms?

Predicting the Crash of Individual Firms Using Complex Theory PaoChung Hsu Ruo-Jie Weng Providence University

 Complex systems is a system, systems with a large number of mutually interacting agents, self-organize their internal structure and sometimes surprising emergent behaviors. (For example, Sornette(2004)) What is a Complex System?

Literature  Johansen and Sornette (2000) apply the complex theory and find that there exists the log-periodic signature before the market crash.

Data  Data ： 90Taiwan Stock Exchange individual firms. (Thirty large firms, thirty small firms and thirty de-listed firms. )  Period ： 2003 to April 30, 2007.  Resource ： Taiwan Economic Journal (TEJ.).

Model  Johansen and Sornette (1999):. 、 price time price time

Model  We apply Hilbert-Huang Transform to test log- periodic signatures in the estimated equation.  If there exists log-periodic signatures in the estimated equation, the Shank’s transformation can be used to estimate the critical time.

Figure a: Estimated Equation of Evertop Corp. Figure b: Hilbert Spectrum of Evertop Corp.

Result Type of firmbubbles Large firm8 Small firm16 De-listed firm11 total35

Result Type of firm Log-periodic signatures of bubbles ExistenceNonexistence Large firm35 Small firm160 De-listed firm83 total278

Result Difference (Days) Large Firm Small Firm De-Listed Firm Total 118312 20213 32215 40303 50134 Total316827

Conclusion  Twenty-seven out of thirty-five bubbles have log- periodic signatures.  The complex theory can explain small firms better.  As long as the log-periodic signature exists in the bubble, then, by using Shank’s Transformation we can forecast the estimated time of the crash.

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